1
|
Manikandan K, Sakkaravarthi K, Sudharsan JB, Aravinthan D. Deformation of optical solitons in a variable-coefficient nonlinear Schrödinger equation with three distinct PT-symmetric potentials and modulated nonlinearities. CHAOS (WOODBURY, N.Y.) 2023; 33:2895997. [PMID: 37307166 DOI: 10.1063/5.0145283] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/04/2023] [Accepted: 05/22/2023] [Indexed: 06/14/2023]
Abstract
We investigate deformed/controllable characteristics of solitons in inhomogeneous parity-time (PT)-symmetric optical media. To explore this, we consider a variable-coefficient nonlinear Schrödinger equation involving modulated dispersion, nonlinearity, and tapering effect with PT-symmetric potential, which governs the dynamics of optical pulse/beam propagation in longitudinally inhomogeneous media. By incorporating three physically interesting and recently identified forms of PT-symmetric potentials, namely, rational, Jacobian periodic, and harmonic-Gaussian potentials, we construct explicit soliton solutions through similarity transformation. Importantly, we investigate the manipulation dynamics of such optical solitons due to diverse inhomogeneities in the medium by implementing step-like, periodic, and localized barrier/well-type nonlinearity modulations and revealing the underlying phenomena. Also, we corroborate the analytical results with direct numerical simulations. Our theoretical exploration will provide further impetus in engineering optical solitons and their experimental realization in nonlinear optics and other inhomogeneous physical systems.
Collapse
Affiliation(s)
- K Manikandan
- Center for Computational Modeling, Chennai Institute of Technology, Chennai 600069, Tamil Nadu, India
| | - K Sakkaravarthi
- Young Scientist Training Program, Asia-Pacific Center for Theoretical Physics (APCTP), POSTECH Campus, Pohang 37673, South Korea
| | - J B Sudharsan
- Center for Computational Modeling, Chennai Institute of Technology, Chennai 600069, Tamil Nadu, India
| | - D Aravinthan
- Center for Computational Modeling, Chennai Institute of Technology, Chennai 600069, Tamil Nadu, India
| |
Collapse
|
2
|
Chen Y, Song J, Li X, Yan Z. Stability and modulation of optical peakons in self-focusing/defocusing Kerr nonlinear media with PT-δ-hyperbolic-function potentials. CHAOS (WOODBURY, N.Y.) 2022; 32:023122. [PMID: 35232047 DOI: 10.1063/5.0080485] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/01/2021] [Accepted: 01/28/2022] [Indexed: 06/14/2023]
Abstract
In this paper, we introduce a class of novel PT- δ-hyperbolic-function potentials composed of the Dirac δ(x) and hyperbolic functions, supporting fully real energy spectra in the non-Hermitian Hamiltonian. The threshold curves of PT symmetry breaking are numerically presented. Moreover, in the self-focusing and defocusing Kerr-nonlinear media, the PT-symmetric potentials can also support the stable peakons, keeping the total power and quasi-power conserved. The unstable PT-symmetric peakons can be transformed into other stable peakons by the excitations of potential parameters. Continuous families of additional stable numerical peakons can be produced in internal modes around the exact peakons (even unstable). Further, we find that the stable peakons can always propagate in a robust form, remaining trapped in the slowly moving potential wells, which opens the way for manipulations of optical peakons. Other significant characteristics related to exact peakons, such as the interaction and power flow, are elucidated in detail. These results will be useful in explaining the related physical phenomena and designing the related physical experiments.
Collapse
Affiliation(s)
- Yong Chen
- School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou 221116, China
| | - Jin Song
- Key Lab of Mathematics Mechanization, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
| | - Xin Li
- School of Mathematics and Statistics, Changshu Institute of Technology, Changshu 215500, China
| | - Zhenya Yan
- Key Lab of Mathematics Mechanization, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
| |
Collapse
|
3
|
Zhong M, Chen Y, Yan Z, Tian SF. Formation, stability, and adiabatic excitation of peakons and double-hump solitons in parity-time-symmetric Dirac-δ(x)-Scarf-II optical potentials. Phys Rev E 2022; 105:014204. [PMID: 35193183 DOI: 10.1103/physreve.105.014204] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/11/2021] [Accepted: 12/17/2021] [Indexed: 06/14/2023]
Abstract
We introduce a class of physically intriguing PT-symmetric Dirac-δ-Scarf-II optical potentials. We find the parameter region making the corresponding non-Hermitian Hamiltonian admit the fully real spectra, and present the stable parameter domains for these obtained peakons, smooth solitons, and double-hump solitons in the self-focusing nonlinear Kerr media with PT-symmetric δ-Scarf-II potentials. In particular, the stable wave propagations are exhibited for the peakon solutions and double-hump solitons from some given parameters even if the corresponding parameters belong to the linear PT-phase broken region. Moreover, we also find the stable wave propagations of exact and numerical peakons and double-hump solitons in the interplay between the power-law nonlinearity and PT-symmetric potentials. Finally, we examine the interactions of the nonlinear modes with exotic waves, and the stable adiabatic excitations of peakons and double-hump solitons in the PT-symmetric Kerr nonlinear media. These results provide the theoretical basis for the design of related physical experiments and applications in PT-symmetric nonlinear optics, Bose-Einstein condensates, and other relevant physical fields.
Collapse
Affiliation(s)
- Ming Zhong
- School of Mathematics, China University of Mining and Technology, Xuzhou 221116, China
| | - Yong Chen
- School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou 221116, China
| | - Zhenya Yan
- Key Lab of Mathematics Mechanization, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
- School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Shou-Fu Tian
- School of Mathematics, China University of Mining and Technology, Xuzhou 221116, China
| |
Collapse
|
4
|
Chen Y, Yan Z, Mihalache D. Soliton formation and stability under the interplay between parity-time-symmetric generalized Scarf-II potentials and Kerr nonlinearity. Phys Rev E 2020; 102:012216. [PMID: 32795035 DOI: 10.1103/physreve.102.012216] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/07/2020] [Accepted: 07/01/2020] [Indexed: 11/07/2022]
Abstract
We present an alternative type of parity-time (PT)-symmetric generalized Scarf-II potentials, which makes possible for non-Hermitian Hamiltonians in the classical linear Schrödinger system to possess fully real spectra with unique features such as the multiple PT-symmetric breaking behaviors and to support one-dimensional (1D) stable PT-symmetric solitons of power-law waveform, namely power-law solitons, in focusing Kerr-type nonlinear media. Moreover, PT-symmetric high-order solitons are also derived numerically in 1D and 2D settings. Around the exactly obtained nonlinear propagation constants, families of 1D and 2D localized nonlinear modes are also found numerically. The majority of fundamental nonlinear modes can still keep steady in general, whereas the 1D multipeak solitons and 2D vortex solitons are usually susceptible to suffering from instability. Likewise, similar results occur in the defocusing Kerr-nonlinear media. The obtained results will be useful for understanding the complex dynamics of nonlinear waves that form in PT-symmetric nonlinear media in other physical contexts.
Collapse
Affiliation(s)
- Yong Chen
- School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou 221116, China
| | - Zhenya Yan
- Key Lab of Mathematics Mechanization, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China.,School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Dumitru Mihalache
- Department of Theoretical Physics, Horia Hulubei National Institute for Physics and Nuclear Engineering, Bucharest-Magurele, RO-077125, Romania
| |
Collapse
|
5
|
Chen Y, Yan Z, Mihalache D. Stable flat-top solitons and peakons in the PT-symmetric δ-signum potentials and nonlinear media. CHAOS (WOODBURY, N.Y.) 2019; 29:083108. [PMID: 31472484 DOI: 10.1063/1.5100294] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/16/2019] [Accepted: 07/18/2019] [Indexed: 06/10/2023]
Abstract
We discover that the physically interesting PT-symmetric Dirac delta-function potentials can not only make sure that the non-Hermitian Hamiltonians admit fully-real linear spectra but also support stable peakons (nonlinear modes) in the Kerr nonlinear Schrödinger equation. For a specific form of the delta-function PT-symmetric potentials, the nonlinear model investigated in this paper is exactly solvable. However, for a class of PT-symmetric signum-function double-well potentials, a novel type of exact flat-top bright solitons can exist stably within a broad range of potential parameters. Intriguingly, the flat-top solitons can be characterized by the finite-order differentiable waveforms and admit the novel features differing from the usual solitons. The excitation features and the direction of transverse power flow of flat-top bright solitons are also explored in detail. These results are useful for the related experimental designs and applications in nonlinear optics and other related fields.
Collapse
Affiliation(s)
- Yong Chen
- School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou 221116, China
| | - Zhenya Yan
- Key Lab of Mathematics Mechanization, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
| | - Dumitru Mihalache
- Horia Hulubei National Institute of Physics and Nuclear Engineering, P.O. Box MG-6, Magurele RO-077125, Romania
| |
Collapse
|
6
|
Wang L, Malomed BA, Yan Z. Attraction centers and parity-time-symmetric delta-functional dipoles in critical and supercritical self-focusing media. Phys Rev E 2019; 99:052206. [PMID: 31212420 DOI: 10.1103/physreve.99.052206] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/19/2019] [Indexed: 11/07/2022]
Abstract
We introduce a model based on the one-dimensional nonlinear Schrödinger equation with critical (quintic) or supercritical self-focusing nonlinearity. We demonstrate that a family of solitons, which are unstable in this setting against the critical or supercritical collapse, is stabilized by pinning to an attractive defect, that may also include a parity-time (PT)-symmetric gain-loss component. The model can be realized as a planar waveguide in nonlinear optics, and in a super-Tonks-Girardeau bosonic gas. For the attractive defect with the delta-functional profile, a full family of the pinned solitons is found in an exact analytical form. In the absence of the gain-loss term, the solitons' stability is investigated in an analytical form too, by means of the Vakhitov-Kolokolov criterion; in the presence of the PT-balanced gain and loss, the stability is explored by means of numerical methods. In particular, the entire family of pinned solitons is stable in the quintic (critical) medium if the gain-loss term is absent. A stability region for the pinned solitons persists in the model with an arbitrarily high power of the self-focusing nonlinearity. A weak gain-loss component gives rise to intricate alternations of stability and instability in the system's parameter plane. Those solitons which are unstable under the action of the supercritical self-attraction are destroyed by the collapse. On the other hand, if the self-attraction-driven instability is weak and the gain-loss term is present, unstable solitons spontaneously transform into localized breathers, while the collapse does not occur. The same outcome may be caused by a combination of the critical nonlinearity with the gain and loss. Instability of the solitons is also possible when the PT-symmetric gain-loss term is added to the subcritical nonlinearity. The system with self-repulsive nonlinearity is briefly considered too, producing completely stable families of pinned localized states.
Collapse
Affiliation(s)
- Li Wang
- Key Laboratory of Mathematics Mechanization, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China.,School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Boris A Malomed
- Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, and Center for Light-Matter Interaction, Tel Aviv University, Tel Aviv 59978, Israel
| | - Zhenya Yan
- Key Laboratory of Mathematics Mechanization, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China.,School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
| |
Collapse
|
7
|
Chen Y, Yan Z, Liu W. Impact of near-𝒫𝒯 symmetry on exciting solitons and interactions based on a complex Ginzburg-Landau model. OPTICS EXPRESS 2018; 26:33022-33034. [PMID: 30645460 DOI: 10.1364/oe.26.033022] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/12/2018] [Accepted: 11/09/2018] [Indexed: 06/09/2023]
Abstract
We theoretically report the influence of a class of near-parity-time-(𝒫𝒯-) symmetric potentials on solitons in the complex Ginzburg-Landau (CGL) equation. Although the linear spectral problem with the potentials does not admit entirely-real spectra due to the existence of spectral filtering parameter α2 or nonlinear gain-loss coefficient β2, we do find stable exact solitons in the second quadrant of the (α2, β2) space including on the corresponding axes. Other fascinating properties associated with the solitons are also examined, such as the interactions and energy flux. Moreover, we study the excitations of nonlinear modes by considering adiabatic changes of parameters in a generalized CGL model. These results are useful for the related experimental designs and applications.
Collapse
|
8
|
Tiofack CGL, Ndzana FI, Mohamadou A, Kofane TC. Spatial solitons and stability in the one-dimensional and the two-dimensional generalized nonlinear Schrödinger equation with fourth-order diffraction and parity-time-symmetric potentials. Phys Rev E 2018; 97:032204. [PMID: 29776102 DOI: 10.1103/physreve.97.032204] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/28/2017] [Indexed: 11/07/2022]
Abstract
We investigate the existence and stability of solitons in parity-time (PT)-symmetric optical media characterized by a generic complex hyperbolic refractive index distribution and fourth-order diffraction (FOD). For the linear case, we demonstrate numerically that the FOD parameter can alter the PT-breaking points. For nonlinear cases, the exact analytical expressions of the localized modes are obtained both in one- and two-dimensional nonlinear Schrödinger equations with self-focusing and self-defocusing Kerr nonlinearity. The effect of FOD on the stability structure of these localized modes is discussed with the help of linear stability analysis followed by the direct numerical simulation of the governing equation. Examples of stable and unstable solutions are given. The transverse power flow density associated with these localized modes is also discussed. It is found that the relative strength of the FOD coefficient can utterly change the direction of the power flow, which may be used to control the energy exchange among gain or loss regions.
Collapse
Affiliation(s)
- C G L Tiofack
- Laboratory of Mechanics, Department of Physics, Faculty of Science, University of Yaounde I, P.O. Box 812, Yaounde, Cameroon.,Centre d'Excellence Africain des Technologies de l'Information et de la Communication (CETIC), University of Yaounde I, P.O. Box 812, Yaounde, Cameroon
| | - F Ii Ndzana
- Laboratory of Mechanics, Department of Physics, Faculty of Science, University of Yaounde I, P.O. Box 812, Yaounde, Cameroon.,Condensed Matter Laboratory, Department of Physics, Faculty of Science, University of Maroua, P.O. Box 814, Maroua, Cameroon.,Centre d'Excellence Africain des Technologies de l'Information et de la Communication (CETIC), University of Yaounde I, P.O. Box 812, Yaounde, Cameroon
| | - A Mohamadou
- Condensed Matter Laboratory, Department of Physics, Faculty of Science, University of Maroua, P.O. Box 814, Maroua, Cameroon.,Centre d'Excellence Africain des Technologies de l'Information et de la Communication (CETIC), University of Yaounde I, P.O. Box 812, Yaounde, Cameroon.,Abdus Salam International Centre for Theoretical Physics, P.O. Box 538, Strada costiera 11, I-34014, Trieste, Italy.,Max Planck Institute for the Physics of Complex Systems, Nothnitzer Strasse 38, 01187, Dresden, Germany
| | - T C Kofane
- Laboratory of Mechanics, Department of Physics, Faculty of Science, University of Yaounde I, P.O. Box 812, Yaounde, Cameroon.,Centre d'Excellence Africain des Technologies de l'Information et de la Communication (CETIC), University of Yaounde I, P.O. Box 812, Yaounde, Cameroon.,Max Planck Institute for the Physics of Complex Systems, Nothnitzer Strasse 38, 01187, Dresden, Germany
| |
Collapse
|
9
|
Yan Z, Chen Y. The nonlinear Schrödinger equation with generalized nonlinearities and PT-symmetric potentials: Stable solitons, interactions, and excitations. CHAOS (WOODBURY, N.Y.) 2017; 27:073114. [PMID: 28764412 DOI: 10.1063/1.4995363] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
We investigate the nonlinear Schrödinger (NLS) equation with generalized nonlinearities and complex non-Hermitian potentials and present the novel parity-time-( PT-) symmetric potentials for the NLS equation with power-law nonlinearities supporting some bright solitons. For distinct types of PT-symmetric potentials including Scarf-II, Hermite-Gaussian, and asymptotically periodic potentials, we, respectively, explore the phase transitions for the linear Hamiltonian operators. Moreover, we analytically find stable bright solitons in the generalized NLS equations with several types of PT-symmetric potentials, and their stability is corroborated by the linear stability spectrum and direct wave-propagation simulations. Interactions of two solitons are also explored. More interestingly, we find that the nonlinearity can excite the unstable linear modes (i.e., possessing broken linear PT-symmetric phase) to stable nonlinear modes. The results may excite potential applications in nonlinear optics, Bose-Einstein condensates, and relevant fields.
Collapse
Affiliation(s)
- Zhenya Yan
- Key Laboratory of Mathematics Mechanization, Institute of Systems Science, AMSS, Chinese Academy of Sciences, Beijing 100190, China and School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Yong Chen
- Key Laboratory of Mathematics Mechanization, Institute of Systems Science, AMSS, Chinese Academy of Sciences, Beijing 100190, China and School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
| |
Collapse
|
10
|
Wen Z, Yan Z. Solitons and their stability in the nonlocal nonlinear Schrödinger equation with PT-symmetric potentials. CHAOS (WOODBURY, N.Y.) 2017; 27:053105. [PMID: 28576099 DOI: 10.1063/1.4982972] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
We report localized nonlinear modes of the self-focusing and defocusing nonlocal nonlinear Schrödinger equation with the generalized PT-symmetric Scarf-II, Rosen-Morse, and periodic potentials. Parameter regions are presented for broken and unbroken PT-symmetric phases of linear bounded states and the linear stability of the obtained solitons. Moreover, we numerically explore the dynamical behaviors of solitons and find stable solitons for some given parameters.
Collapse
Affiliation(s)
- Zichao Wen
- Key Laboratory of Mathematics Mechanization, Institute of Systems Science, AMSS, Chinese Academy of Sciences, Beijing 100190, China
| | - Zhenya Yan
- Key Laboratory of Mathematics Mechanization, Institute of Systems Science, AMSS, Chinese Academy of Sciences, Beijing 100190, China
| |
Collapse
|
11
|
Chen Y, Yan Z, Mihalache D, Malomed BA. Families of stable solitons and excitations in the PT-symmetric nonlinear Schrödinger equations with position-dependent effective masses. Sci Rep 2017; 7:1257. [PMID: 28455499 PMCID: PMC5430832 DOI: 10.1038/s41598-017-01401-3] [Citation(s) in RCA: 37] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/05/2017] [Accepted: 03/29/2017] [Indexed: 11/09/2022] Open
Abstract
Since the parity-time-([Formula: see text]-) symmetric quantum mechanics was put forward, fundamental properties of some linear and nonlinear models with [Formula: see text]-symmetric potentials have been investigated. However, previous studies of [Formula: see text]-symmetric waves were limited to constant diffraction coefficients in the ambient medium. Here we address effects of variable diffraction coefficient on the beam dynamics in nonlinear media with generalized [Formula: see text]-symmetric Scarf-II potentials. The broken linear [Formula: see text] symmetry phase may enjoy a restoration with the growing diffraction parameter. Continuous families of one- and two-dimensional solitons are found to be stable. Particularly, some stable solitons are analytically found. The existence range and propagation dynamics of the solitons are identified. Transformation of the solitons by means of adiabatically varying parameters, and collisions between solitons are studied too. We also explore the evolution of constant-intensity waves in a model combining the variable diffraction coefficient and complex potentials with globally balanced gain and loss, which are more general than [Formula: see text]-symmetric ones, but feature similar properties. Our results may suggest new experiments for [Formula: see text]-symmetric nonlinear waves in nonlinear nonuniform optical media.
Collapse
Affiliation(s)
- Yong Chen
- Key Laboratory of Mathematics Mechanization, Institute of Systems Science, AMSS, Chinese Academy of Sciences, Beijing, 100190, China
- School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, 100049, China
| | - Zhenya Yan
- Key Laboratory of Mathematics Mechanization, Institute of Systems Science, AMSS, Chinese Academy of Sciences, Beijing, 100190, China.
- School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, 100049, China.
| | - Dumitru Mihalache
- Department of Theoretical Physics, Horia Hulubei National Institute of Physics and Nuclear Engineering, PO Box MG-6, Bucharest, Romania
| | - Boris A Malomed
- Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv, 59978, Israel
- Laboratory of Nonlinear-Optical Informatics, ITMO University, St. Petersburg, 197101, Russia
| |
Collapse
|
12
|
Chen Y, Yan Z. Stable parity-time-symmetric nonlinear modes and excitations in a derivative nonlinear Schrödinger equation. Phys Rev E 2017; 95:012205. [PMID: 28208375 DOI: 10.1103/physreve.95.012205] [Citation(s) in RCA: 25] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/21/2016] [Indexed: 11/07/2022]
Abstract
The effect of derivative nonlinearity and parity-time-symmetric (PT-symmetric) potentials on the wave propagation dynamics is explored in the derivative nonlinear Schrödinger equation, where the physically interesting Scarf-II and harmonic-Hermite-Gaussian potentials are chosen. We study numerically the regions of unbroken and broken linear PT-symmetric phases and find some stable bright solitons of this model in a wide range of potential parameters even though the corresponding linear PT-symmetric phases are broken. The semielastic interactions between particular bright solitons and exotic incident waves are illustrated such that we find that particular nonlinear modes almost keep their shapes after interactions even if the exotic incident waves have evidently been changed. Moreover, we exert the adiabatic switching on PT-symmetric potential parameters such that a stable nonlinear mode with the unbroken linear PT-symmetric phase can be excited to another stable nonlinear mode belonging to the broken linear PT-symmetric phase.
Collapse
Affiliation(s)
- Yong Chen
- Key Laboratory of Mathematics Mechanization, Institute of Systems Science, AMSS, Chinese Academy of Sciences, Beijing 100190, China and University of Chinese Academy of Sciences, Beijing 100049, China
| | - Zhenya Yan
- Key Laboratory of Mathematics Mechanization, Institute of Systems Science, AMSS, Chinese Academy of Sciences, Beijing 100190, China and University of Chinese Academy of Sciences, Beijing 100049, China
| |
Collapse
|
13
|
Li X, Yan Z. Stability, integrability, and nonlinear dynamics of PT-symmetric optical couplers with cubic cross-interactions or cubic-quintic nonlinearities. CHAOS (WOODBURY, N.Y.) 2017; 27:013105. [PMID: 28147490 DOI: 10.1063/1.4973413] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
We explore the parity-time-( PT)-symmetric optical couplers with the cubic both self- and cross-interactions corresponding to self- and cross-phase modulations. When the coefficient of the cubic cross-interaction is chosen as the different values, we find three distinct cases for two branches, including the stable-stable modes (linear unbroken PT-symmetric phase), stable-unstable modes (linear unbroken PT-symmetric phase), as well as unstable-unstable modes (linear broken PT-symmetric phase). Moreover, we find the periodic trajectories for some parameters. Similarly, we also explore the PT-symmetric optical couplers with cubic-quintic self-phase modulations. We numerically give the stable and unstable regions of the cubic-quintic system. Moreover, we also find the periodic trajectories for some parameters in the Stokes domain.
Collapse
Affiliation(s)
- Xin Li
- Key Laboratory of Mathematics Mechanization, Institute of Systems Science, AMSS, Chinese Academy of Sciences, Beijing 100190, China
| | - Zhenya Yan
- Key Laboratory of Mathematics Mechanization, Institute of Systems Science, AMSS, Chinese Academy of Sciences, Beijing 100190, China
| |
Collapse
|
14
|
Yan Z, Chen Y, Wen Z. On stable solitons and interactions of the generalized Gross-Pitaevskii equation with PT- and non- PT-symmetric potentials. CHAOS (WOODBURY, N.Y.) 2016; 26:083109. [PMID: 27586605 DOI: 10.1063/1.4960612] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
We report the bright solitons of the generalized Gross-Pitaevskii (GP) equation with some types of physically relevant parity-time- ( PT-) and non- PT-symmetric potentials. We find that the constant momentum coefficient Γ can modulate the linear stability and complicated transverse power-flows (not always from the gain toward loss) of nonlinear modes. However, the varying momentum coefficient Γ(x) can modulate both unbroken linear PT-symmetric phases and stability of nonlinear modes. Particularly, the nonlinearity can excite the unstable linear mode (i.e., broken linear PT-symmetric phase) to stable nonlinear modes. Moreover, we also find stable bright solitons in the presence of non- PT-symmetric harmonic-Gaussian potential. The interactions of two bright solitons are also illustrated in PT-symmetric potentials. Finally, we consider nonlinear modes and transverse power-flows in the three-dimensional (3D) GP equation with the generalized PT-symmetric Scarff-II potential.
Collapse
Affiliation(s)
- Zhenya Yan
- Key Laboratory of Mathematics Mechanization, Institute of Systems Science, AMSS, Chinese Academy of Sciences, Beijing 100190, China
| | - Yong Chen
- Key Laboratory of Mathematics Mechanization, Institute of Systems Science, AMSS, Chinese Academy of Sciences, Beijing 100190, China
| | - Zichao Wen
- Key Laboratory of Mathematics Mechanization, Institute of Systems Science, AMSS, Chinese Academy of Sciences, Beijing 100190, China
| |
Collapse
|