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Alonso-Izquierdo A, Navarro-Obregón S, Oles K, Queiruga J, Romanczukiewicz T, Wereszczynski A. Semi-Bogomol'nyi-Prasad-Sommerfield sphaleron and its dynamics. Phys Rev E 2023; 108:064208. [PMID: 38243486 DOI: 10.1103/physreve.108.064208] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/09/2023] [Accepted: 11/27/2023] [Indexed: 01/21/2024]
Abstract
We construct a simple field theory in which a sphaleron, i.e., a saddle-point particle-like solution, forms a semi-BPS state with a background defect that is an impurity. This means that there is no static force between the sphaleron and the impurity. Therefore, such a sphaleron-impurity system is very much like usual BPS multisolitons, however, still possessing an unstable direction allowing for its decay. We study dynamics of the sphaleron in such a system.
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Affiliation(s)
- A Alonso-Izquierdo
- Department of Applied Mathematics, University of Salamanca, Casas del Parque 2 and Institute of Fundamental Physics and Mathematics, University of Salamanca, Plaza de la Merced 1, 37008-Salamanca, Spain
| | - S Navarro-Obregón
- Departamento de Física Teórica, Atómica y Óptica, Universidad de Valladolid, 47011 Valladolid, Spain
| | - K Oles
- Institute of Theoretical Physics, Jagiellonian University, Lojasiewicza 11, Kraków, Poland
| | - J Queiruga
- Department of Applied Mathematics, University of Salamanca, Casas del Parque 2 and Institute of Fundamental Physics and Mathematics, University of Salamanca, Plaza de la Merced 1, 37008-Salamanca, Spain
| | - T Romanczukiewicz
- Institute of Theoretical Physics, Jagiellonian University, Lojasiewicza 11, Kraków, Poland
| | - A Wereszczynski
- Institute of Theoretical Physics, Jagiellonian University, Lojasiewicza 11, Kraków, Poland
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2
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Adam C, Oles K, Romanczukiewicz T, Wereszczynski A. Spectral Walls in Soliton Collisions. PHYSICAL REVIEW LETTERS 2019; 122:241601. [PMID: 31322394 DOI: 10.1103/physrevlett.122.241601] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/04/2019] [Revised: 05/10/2019] [Indexed: 06/10/2023]
Abstract
During defect-antidefect scattering, bound modes frequently disappear into the continuous spectrum before the defects themselves collide. This leads to a structural, nonperturbative change in the spectrum of small excitations. Sometimes the effect can be seen as a hard wall from which the defect can bounce off. We show the existence of these spectral walls and study their properties in the ϕ^{4} model with Bogomol'nyi-Prasad-Sommerfield preserving impurity, where the spectral wall phenomenon can be isolated because the static force between the antikink and the impurity vanishes. We conclude that such spectral walls should surround all solitons possessing internal modes.
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Affiliation(s)
- C Adam
- Departamento de Física de Partículas, Universidad de Santiago de Compostela and Instituto Galego de Física de Altas Enerxias (IGFAE), E-15782 Santiago de Compostela, Spain
| | - K Oles
- Institute of Physics, Jagiellonian University, Lojasiewicza 11, Kraków 31-007, Poland
| | - T Romanczukiewicz
- Institute of Physics, Jagiellonian University, Lojasiewicza 11, Kraków 31-007, Poland
| | - A Wereszczynski
- Institute of Physics, Jagiellonian University, Lojasiewicza 11, Kraków 31-007, Poland
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3
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Goodman RH, Rahman A, Bellanich MJ, Morrison CN. A mechanical analog of the two-bounce resonance of solitary waves: Modeling and experiment. CHAOS (WOODBURY, N.Y.) 2015; 25:043109. [PMID: 25933657 DOI: 10.1063/1.4917047] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
We describe a simple mechanical system, a ball rolling along a specially-designed landscape, which mimics the well-known two-bounce resonance in solitary wave collisions, a phenomenon that has been seen in countless numerical simulations but never in the laboratory. We provide a brief history of the solitary wave problem, stressing the fundamental role collective-coordinate models played in understanding this phenomenon. We derive the equations governing the motion of a point particle confined to such a surface and then design a surface on which to roll the ball, such that its motion will evolve under the same equations that approximately govern solitary wave collisions. We report on physical experiments, carried out in an undergraduate applied mathematics course, that seem to exhibit the two-bounce resonance.
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Affiliation(s)
- Roy H Goodman
- Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, New Jersey 07102
| | - Aminur Rahman
- Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, New Jersey 07102
| | - Michael J Bellanich
- Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, New Jersey 07102
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4
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Saadatmand D, Dmitriev SV, Borisov DI, Kevrekidis PG. Interaction of sine-Gordon kinks and breathers with a parity-time-symmetric defect. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:052902. [PMID: 25493853 DOI: 10.1103/physreve.90.052902] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/11/2014] [Indexed: 06/04/2023]
Abstract
The scattering of kinks and low-frequency breathers of the nonlinear sine-Gordon (SG) equation on a spatially localized parity-time-symmetric perturbation (defect) with a balanced gain and loss is investigated numerically. It is demonstrated that if a kink passes the defect, it always restores its initial momentum and energy, and the only effect of the interaction with the defect is a phase shift of the kink. A kink approaching the defect from the gain side always passes, while in the opposite case it must have sufficiently large initial momentum to pass through the defect instead of being trapped in the loss region. The kink phase shift and critical velocity are calculated by means of the collective variable method. Kink-kink (kink-antikink) collisions at the defect are also briefly considered, showing how their pairwise repulsive (respectively, attractive) interaction can modify the collisional outcome of a single kink within the pair with the defect. For the breather, the result of its interaction with the defect depends strongly on the breather parameters (velocity, frequency, and initial phase) and on the defect parameters. The breather can gain some energy from the defect and as a result potentially even split into a kink-antikink pair, or it can lose a part of its energy. Interestingly, the breather translational mode is very weakly affected by the dissipative perturbation, so that a breather penetrates more easily through the defect when it comes from the lossy side, than a kink. In all studied soliton-defect interactions, the energy loss to radiation of small-amplitude extended waves is negligible.
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Affiliation(s)
- Danial Saadatmand
- Department of Physics, Ferdowsi University of Mashhad, 91775-1436 Mashhad, Iran
| | - Sergey V Dmitriev
- Institute for Metals Superplasticity Problems RAS, Khalturin 39, 450001 Ufa, Russia and Saint Petersburg State Polytechnical University, Politekhnicheskaya 29, 195251 St. Petersburg, Russia
| | - Denis I Borisov
- Institute of Mathematics CC USC RAS, Chernyshevsky 112, 450008 Ufa, Russia and Bashkir State Pedagogical University, October Rev. 3a, 450000 Ufa, Russia
| | - Panayotis G Kevrekidis
- Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003, USA
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5
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Vanitha M, Daniel M. Internal nonlinear dynamics of a short lattice DNA model in terms of propagating kink-antikink solitons. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:041911. [PMID: 22680502 DOI: 10.1103/physreve.85.041911] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/27/2011] [Revised: 03/09/2012] [Indexed: 06/01/2023]
Abstract
We study the internal nonlinear dynamics of an inhomogeneous short lattice DNA model by solving numerically the governing discrete perturbed sine-Gordon equations under the limits of a uniform and a nonuniform angular rotation of bases. The internal dynamics is expressed in terms of open-state configurations represented by kink and antikink solitons with fluctuations. The inhomogeneity in the strands and hydrogen bonds as well as nonuniformity in the rotation of bases introduce fluctuations in the profile of the solitons without affecting their robust nature and the propagation. These fluctuations spread into the tail regions of the soliton in the case of periodic inhomogeneity. However, the localized form of inhomogeneity generates amplified fluctuations in the profile of the soliton. The fluctuations are expected to enhance the denaturation process in the DNA molecule.
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Affiliation(s)
- M Vanitha
- Centre for Nonlinear Dynamics, School of Physics, Bharathidasan University, Tiruchirapalli 620 024, India
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Gredeskul SA, Derevyanko SA, Kovalev AS, Prilepsky JE. Soliton propagation through a disordered system: statistics of the transmission delay. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 81:036608. [PMID: 20365897 DOI: 10.1103/physreve.81.036608] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/26/2009] [Indexed: 05/29/2023]
Abstract
We have studied the soliton propagation through a segment containing random pointlike scatterers. In the limit of small concentration of scatterers when the mean distance between the scatterers is larger than the soliton width, a method has been developed for obtaining the statistical characteristics of the soliton transmission through the segment. The method is applicable for any classical particle traversing through a disordered segment with the given velocity transformation after each act of scattering. In the case of weak scattering and relatively short disordered segment the transmission time delay of a fast soliton is mostly determined by the shifts of the soliton center after each act of scattering. For sufficiently long segments the main contribution to the delay is due to the shifts of the amplitude and velocity of a fast soliton after each scatterer. Corresponding crossover lengths for both cases of light and heavy solitons have been obtained. We have also calculated the exact probability density function of the soliton transmission time delay for a sufficiently long segment. In the case of weak identical scatterers the latter is a universal function which depends on a sole parameter--the mean number of scatterers in a segment.
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Affiliation(s)
- Sergey A Gredeskul
- Department of Physics, Ben Gurion University of Negev, Beer Sheva, Israel
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7
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Piette B, Zakrzewski WJ. Scattering of sine-Gordon breathers on a potential well. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 79:046603. [PMID: 19518367 DOI: 10.1103/physreve.79.046603] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/17/2008] [Indexed: 05/27/2023]
Abstract
We analyze the scattering of the classical sine-Gordon breathers on a square potential well. We show that the scattering process depends not only on the vibration frequency of the breather and its incoming speed but also on its phase as well as the depth and width of the well. We show that the breather can pass through the well and exit with a speed different, sometimes larger, from the initial one. It can also be trapped and very slowly decay inside the well or bounce out of the well and go back to where it came from. We also show that the breather can split into a kink-antikink pair when it hits the well.
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Affiliation(s)
- B Piette
- Department of Mathematical Sciences, University of Durham, Durham DH1 3LE, United Kingdom.
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8
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Goodman RH. Chaotic scattering in solitary wave interactions: a singular iterated-map description. CHAOS (WOODBURY, N.Y.) 2008; 18:023113. [PMID: 18601480 DOI: 10.1063/1.2904823] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/26/2023]
Abstract
We derive a family of singular iterated maps--closely related to Poincare maps--that describe chaotic interactions between colliding solitary waves. The chaotic behavior of such solitary-wave collisions depends on the transfer of energy to a secondary mode of oscillation, often an internal mode of the pulse. This map allows us to go beyond previous analyses and to understand the interactions in the case when this mode is excited prior to the first collision. The map is derived using Melnikov integrals and matched asymptotic expansions and generalizes a "multipulse" Melnikov integral. It allows one to find not only multipulse heteroclinic orbits, but exotic periodic orbits. The maps exhibit singular behavior, including regions of infinite winding. These maps are shown to be singular versions of the conservative Ikeda map from laser physics and connections are made with problems from celestial mechanics and fluid mechanics.
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Affiliation(s)
- Roy H Goodman
- Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, New Jersey 07102, USA
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9
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Zhu Y, Haberman R, Yang J. Universal map for fractal structures in weak interactions of solitary waves. PHYSICAL REVIEW LETTERS 2008; 100:143901. [PMID: 18518032 DOI: 10.1103/physrevlett.100.143901] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/21/2007] [Indexed: 05/26/2023]
Abstract
Fractal scatterings in weak solitary-wave interactions are analyzed for generalized nonlinear Schrödiger equations (GNLS). Using asymptotic methods, these weak interactions are reduced to a universal second-order map. This map gives the same fractal-scattering patterns as those in the GNLS equations both qualitatively and quantitatively. Scaling laws of these fractals are also derived.
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Affiliation(s)
- Yi Zhu
- Zhou Pei-Yuan Center for Applied Mathematics, Tsinghua University, Beijing 100084, China
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10
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Goodman RH, Haberman R. Chaotic scattering and the n-bounce resonance in solitary-wave interactions. PHYSICAL REVIEW LETTERS 2007; 98:104103. [PMID: 17358538 DOI: 10.1103/physrevlett.98.104103] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/21/2006] [Indexed: 05/14/2023]
Abstract
We present a new and complete analysis of the n-bounce resonance and chaotic scattering in solitary-wave collisions. In these phenomena, the speed at which a wave exits a collision depends in a complicated fractal way on its input speed. We present a new asymptotic analysis of collective-coordinate ordinary differential equations (ODEs), reduced models that reproduce the dynamics of these systems. We reduce the ODEs to discrete-time iterated separatrix maps and obtain new quantitative results unraveling the fractal structure of the scattering behavior. These phenomena have been observed repeatedly in many solitary-wave systems over 25 years.
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Affiliation(s)
- Roy H Goodman
- Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, New Jersey 07102, USA.
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11
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Zhu Y, Yang J. Universal fractal structures in the weak interaction of solitary waves in generalized nonlinear Schrödinger equations. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 75:036605. [PMID: 17500807 DOI: 10.1103/physreve.75.036605] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/05/2006] [Indexed: 05/15/2023]
Abstract
Weak interactions of solitary waves in the generalized nonlinear Schrödinger equations are studied. It is first shown that these interactions exhibit similar fractal dependence on initial conditions for different nonlinearities. Then by using the Karpman-Solov'ev method, a universal system of dynamical equations is derived for the velocities, amplitudes, positions, and phases of interacting solitary waves. These dynamical equations contain a single parameter, which accounts for the different forms of nonlinearity. When this parameter is zero, these dynamical equations are integrable, and the exact analytical solutions are derived. When this parameter is nonzero, the dynamical equations exhibit fractal structures which match those in the original wave equations both qualitatively and quantitatively. Thus the universal nature of fractal structures in the weak interaction of solitary waves is analytically established. The origin of these fractal structures is also explored. It is shown that these structures bifurcate from the initial conditions where the solutions of the integrable dynamical equations develop finite-time singularities. Based on this observation, an analytical criterion for the existence and locations of fractal structures is obtained. Lastly, these analytical results are applied to the generalized nonlinear Schrödinger equations with various nonlinearities such as the saturable nonlinearity, and predictions on their weak interactions of solitary waves are made.
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Affiliation(s)
- Yi Zhu
- Zhou Pei-Yuan Center for Applied Mathematics, Tsinghua University, Beijing 100084, People's Republic of China.
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Stoychev KT, Primatarowa MT, Kamburova RS. Interaction of solitons with segments with modified dispersion. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 73:066611. [PMID: 16907001 DOI: 10.1103/physreve.73.066611] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/14/2006] [Indexed: 05/11/2023]
Abstract
The interaction of nonlinear Schrödinger solitons with extended inhomogeneities with modified group-velocity (GV) and group-velocity dispersion (GVD) coefficients is investigated numerically. Increased GVD coefficients act as potential barriers and yield reflection or transmission of the incoming soliton. Decreased GVD coefficients act as potential wells, and for a given range of parameters the scattering results exhibit periodically repeating windows of trapping and transmission as a function of the length of the segment. It is shown that the escape of the soliton is due to a resonance between the period of the shape oscillations of the soliton inside the segment and the length of the latter. Segments with modified GV coefficients act as potential wells for both positive and negative values of the GV mismatch and can also lead to periodic capture-transmission scattering patterns.
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Affiliation(s)
- K T Stoychev
- Institute of Solid State Physics, Bulgarian Academy of Sciences, 1784 Sofia, Bulgaria
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Primatarowa MT, Stoychev KT, Kamburova RS. Interaction of solitons with extended nonlinear defects. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 72:036608. [PMID: 16241593 DOI: 10.1103/physreve.72.036608] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/27/2005] [Indexed: 05/05/2023]
Abstract
The interaction of nonlinear Schrödinger solitons with extended inhomogeneities with modified nonlinear coefficients is investigated numerically. Decreased nonlinear coefficients act as nonlinear potential steps and yield transmission or reflection of the incoming soliton. For increased nonlinear coefficients (nonlinear potential wells) and a given range of initial velocities and nonlinearity mismatch, the scattering pattern exhibits periodically repeating regions of trapping and transmission as a function of the length of the inhomogeneity. It is shown that the escape of the soliton is due to a resonance between the period of the shape oscillations of the soliton inside the inhomogeneity and the length of the latter. The combined effect of overlapping linear and nonlinear potentials is also investigated.
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Affiliation(s)
- M T Primatarowa
- Institute of Solid State Physics, Bulgarian Academy of Sciences, 1784 Sofia, Bulgaria
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Kartashov YV, Vysloukh VA. Anderson localization of solitons in optical lattices with random frequency modulation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 72:026606. [PMID: 16196734 DOI: 10.1103/physreve.72.026606] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/06/2005] [Indexed: 05/04/2023]
Abstract
We report on the phenomenon of Anderson-type localization of walking solitons in optical lattices with random frequency modulation, manifested as dramatic enhancement of soliton trapping probability on lattice inhomogeneities with the growth of the frequency fluctuation level. The localization process is strongly sensitive to the lattice depth since in shallow lattices walking solitons experience random refraction and/or multiple scattering in contrast to relatively deep lattices, where solitons are typically immobilized in the vicinity of local minimums of modulation frequency.
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Affiliation(s)
- Yaroslav V Kartashov
- ICFO-Institut de Ciencies Fotoniques and Universitat Politecnica de Catalunya, 08034, Barcelona, Spain
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15
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Goodman RH, Haberman R. Vector-soliton collision dynamics in nonlinear optical fibers. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 71:056605. [PMID: 16089666 DOI: 10.1103/physreve.71.056605] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/08/2004] [Indexed: 05/03/2023]
Abstract
We consider the interactions of two identical, orthogonally polarized vector solitons in a nonlinear optical fiber with two polarization directions, described by a coupled pair of nonlinear Schrödinger equations. We study a low-dimensional model system of Hamiltonian ordinary differential equations (ODEs) derived by Ueda and Kath and also studied by Tan and Yang. We derive a further simplified model which has similar dynamics but is more amenable to analysis. Sufficiently fast solitons move by each other without much interaction, but below a critical velocity the solitons may be captured. In certain bands of initial velocities the solitons are initially captured, but separate after passing each other twice, a phenomenon known as the two-bounce or two-pass resonance. We derive an analytic formula for the critical velocity. Using matched asymptotic expansions for separatrix crossing, we determine the location of these "resonance windows." Numerical simulations of the ODE models show they compare quite well with the asymptotic theory.
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Affiliation(s)
- Roy H Goodman
- Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, New Jersey 07102, USA.
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16
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Stoychev KT, Primatarowa MT, Kamburova RS. Resonant scattering of nonlinear Schrödinger solitons from potential wells. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 70:066622. [PMID: 15697541 DOI: 10.1103/physreve.70.066622] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/05/2003] [Revised: 06/23/2004] [Indexed: 05/24/2023]
Abstract
The interaction of nonlinear Schrödinger solitons with extended inhomogeneities, modeled by potential wells with different shapes, is investigated numerically. For fixed initial velocities below the transmission threshold, the scattering pattern as a function of the width of the well exhibits periodically repeating regions of trapping, transmission, and reflection. The observed effects are associated with excitation and a following resonant deexcitation (in the cases of escape) of shape oscillations of the solitons at the well boundaries. The analysis of the oscillations indicates that they are due to interference of the solitons with emitted dispersive waves.
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Affiliation(s)
- K T Stoychev
- Institute of Solid State Physics, Bulgarian Academy of Sciences, 1784 Sofia, Bulgaria
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Cuevas J, Palmero F, Archilla JFR, Romero FR. Moving discrete breathers in a Klein Gordon chain with an impurity. ACTA ACUST UNITED AC 2002. [DOI: 10.1088/0305-4470/35/49/302] [Citation(s) in RCA: 38] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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18
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Bronski JC, Segev M, Weinstein MI. Mathematical frontiers in optical solitons. Proc Natl Acad Sci U S A 2001; 98:12872-3. [PMID: 11687646 PMCID: PMC60789 DOI: 10.1073/pnas.231499298] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Solitons are localized concentrations of field energy, resulting from a balance of dispersive and nonlinear effects. They are ubiquitous in the natural sciences. In recent years optical solitons have arisen in new and exciting contexts that differ in many ways from the original context of coherent propagation in a uniform medium. We review recent developments in incoherent spatial solitons and in gap solitons in periodic structures.
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Affiliation(s)
- J C Bronski
- Department of Mathematics, University of Illinois, 1409 West Green, Urbana, IL 61820, USA
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19
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Zhang F, Collins MA, Kivshar YS. Kinks and conformational defects in nonlinear chains. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1995; 51:3774-3777. [PMID: 9963066 DOI: 10.1103/physreve.51.3774] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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20
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Forinash K, Peyrard M, Malomed B. Interaction of discrete breathers with impurity modes. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1994; 49:3400-3411. [PMID: 9961608 DOI: 10.1103/physreve.49.3400] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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21
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Fei Z, Kivshar YS, Vázquez L. Resonant kink-impurity interactions in the phi4 model. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1992; 46:5214-5220. [PMID: 9908743 DOI: 10.1103/physreva.46.5214] [Citation(s) in RCA: 28] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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