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Talukdar S, Dutta R, Kumar Saharia G, Nandy S. Systematic soliton shape modulation by engineering superposed plane wave and soliton parameters. CHAOS (WOODBURY, N.Y.) 2024; 34:083108. [PMID: 39121000 DOI: 10.1063/5.0218438] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/11/2024] [Accepted: 07/22/2024] [Indexed: 08/11/2024]
Abstract
We investigate the linear interference of a plane wave with different localized waves using the coupled Fokas-Lenells equation (FLE) with four-wave mixing term. We obtain the localized wave solution of the coupled FLE by linear superposition of two distinctly independent wave solutions, namely, the plane wave and one soliton solution and the plane wave and two soliton solution. We obtain several nonlinear profiles depending on the relative phase induced by soliton parameters. We present a systematic analysis of the linear interference profile under four different conditions on the spatial and temporal phase coefficients of interfering waves. We further investigate the interaction of two soliton solution and a plane wave. In this case, we find that, asymptotically, two soliton profiles may be similar or different from each other depending on the choices of soliton parameters in the two cases. The present analysis may also be applied to study the linear interference pattern of other localized waves. We believe that the results obtained by us shall be useful in soliton control, all-optical switching, and optical computing.
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Affiliation(s)
| | - Riki Dutta
- Department of Physics, Cotton University, Guwahati 781001, Assam, India
| | | | - Sudipta Nandy
- Department of Physics, Cotton University, Guwahati 781001, Assam, India
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Qin YH, Zhao LC, Yang ZQ, Ling L. Multivalley dark solitons in multicomponent Bose-Einstein condensates with repulsive interactions. Phys Rev E 2021; 104:014201. [PMID: 34412198 DOI: 10.1103/physreve.104.014201] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/12/2021] [Accepted: 06/09/2021] [Indexed: 06/13/2023]
Abstract
We obtain multivalley dark soliton solutions with asymmetric or symmetric profiles in multicomponent repulsive Bose-Einstein condensates by developing the Darboux transformation method. We demonstrate that the width-dependent parameters of solitons significantly affect the velocity ranges and phase jump regions of multivalley dark solitons, in sharp contrast to scalar dark solitons. For double-valley dark solitons, we find that the phase jump is in the range [0,2π], which is quite different from that of the usual single-valley dark soliton. Based on our results, we argue that the phase jump of an n-valley dark soliton could be in the range [0,nπ], supported by our analysis extending up to five-component condensates. The interaction between a double-valley dark soliton and a single-valley dark soliton is further investigated, and we reveal a striking collision process in which the double-valley dark soliton is transformed into a breather after colliding with the single-valley dark soliton. Our analyses suggest that this breather transition exists widely in the collision processes involving multivalley dark solitons. The possibilities for observing these multivalley dark solitons in related Bose-Einstein condensates experiments are discussed.
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Affiliation(s)
- Yan-Hong Qin
- School of Physics, Northwest University, Xi'an 710127, China
- Shaanxi Key Laboratory for Theoretical Physics Frontiers, Xi'an 710127, China
| | - Li-Chen Zhao
- School of Physics, Northwest University, Xi'an 710127, China
- NSFC-SPTP Peng Huanwu Center for Fundamental Theory, Xi'an 710127, China
- Shaanxi Key Laboratory for Theoretical Physics Frontiers, Xi'an 710127, China
| | - Zeng-Qiang Yang
- Department of Physics, School of Arts and Sciences, Shaanxi University of Science and Technology, Xi'an 710021, China
| | - Liming Ling
- School of Mathematics, South China University of Technology, Guangzhou 510640, China
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Sun WR, Wang L. Matter rogue waves for the three-component Gross-Pitaevskii equations in the spinor Bose-Einstein condensates. Proc Math Phys Eng Sci 2018; 474:20170276. [PMID: 29434501 DOI: 10.1098/rspa.2017.0276] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/13/2017] [Accepted: 11/29/2017] [Indexed: 11/12/2022] Open
Abstract
To show the existence and properties of matter rogue waves in an F=1 spinor Bose-Einstein condensate (BEC), we work on the three-component Gross-Pitaevskii (GP) equations. Via the Darboux-dressing transformation, we obtain a family of rational solutions describing the extreme events, i.e. rogue waves. This family of solutions includes bright-dark-bright and bright-bright-bright rogue waves. The algebraic construction depends on Lax matrices and their Jordan form. The conditions for the existence of rogue wave solutions in an F=1 spinor BEC are discussed. For the three-component GP equations, if there is modulation instability, it is of baseband type only, confirming our analytic conditions. The energy transfers between the waves are discussed.
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Affiliation(s)
- Wen-Rong Sun
- School of Mathematics and Physics, Composite and Interface Science, University of Science and Technology Beijing, Beijing 100083, People's Republic of China.,Beijing Key Laboratory for Magneto-Photoelectrical, Composite and Interface Science, University of Science and Technology Beijing, Beijing 100083, People's Republic of China
| | - Lei Wang
- Department of Mathematics and Physics, North China Electric Power University, Beijing 102206, People's Republic of China
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Wang X, Liu C, Wang L. Rogue waves and W-shaped solitons in the multiple self-induced transparency system. CHAOS (WOODBURY, N.Y.) 2017; 27:093106. [PMID: 28964150 DOI: 10.1063/1.4986609] [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 study localized nonlinear waves on a plane wave background in the multiple self-induced transparency (SIT) system, which describes an important enhancement of the amplification and control of optical waves compared to the single SIT system. A hierarchy of exact multiparametric rational solutions in a compact determinant representation is presented. We demonstrate that this family of solutions contain known rogue wave solutions and unusual W-shaped soliton solutions. State transitions between the fundamental rogue waves and W-shaped solitons as well as higher-order nonlinear superposition modes are revealed in the zero-frequency perturbation region by the suitable choice for the background wavenumber of the electric field component. Particularly, it is found that the multiple SIT system can admit both stationary and nonstationary W-shaped solitons in contrast to the stationary results in the single SIT system. Moreover, the W-shaped soliton complex which is formed by a certain number of fundamental W-shaped solitons with zero phase parameters and its decomposition mechanism in the case of the nonzero phase parameters are shown. Meanwhile, some important characteristics of the nonlinear waves including trajectories and spectrum are discussed through the numerical and analytical methods.
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Affiliation(s)
- Xin Wang
- College of Science, Zhongyuan University of Technology, Zhengzhou 450007, China
| | - Chong Liu
- School of Physics, Northwest University, Xi'an 710069, China
| | - Lei Wang
- School of Mathematics and Physics, North China Electric Power University, Beijing 102206, China
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Wang L, Zhang JH, Wang ZQ, Liu C, Li M, Qi FH, Guo R. Breather-to-soliton transitions, nonlinear wave interactions, and modulational instability in a higher-order generalized nonlinear Schrödinger equation. Phys Rev E 2016; 93:012214. [PMID: 26871080 DOI: 10.1103/physreve.93.012214] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/26/2015] [Indexed: 06/05/2023]
Abstract
We study the nonlinear waves on constant backgrounds of the higher-order generalized nonlinear Schrödinger (HGNLS) equation describing the propagation of ultrashort optical pulse in optical fibers. We derive the breather, rogue wave, and semirational solutions of the HGNLS equation. Our results show that these three types of solutions can be converted into the nonpulsating soliton solutions. In particular, we present the explicit conditions for the transitions between breathers and solitons with different structures. Further, we investigate the characteristics of the collisions between the soliton and breathers. Especially, based on the semirational solutions of the HGNLS equation, we display the novel interactions between the rogue waves and other nonlinear waves. In addition, we reveal the explicit relation between the transition and the distribution characteristics of the modulation instability growth rate.
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Affiliation(s)
- Lei Wang
- Department of Mathematics and Physics, North China Electric Power University, Beijing 102206, P. R. China
| | - Jian-Hui Zhang
- School of Energy Power and Mechanical Engneering, North China Electric Power University, Beijing 102206, P. R. China
| | - Zi-Qi Wang
- School of Energy Power and Mechanical Engneering, North China Electric Power University, Beijing 102206, P. R. China
| | - Chong Liu
- School of Physics, Northwest University, Xi'an 710069, P. R. China
| | - Min Li
- Department of Mathematics and Physics, North China Electric Power University, Beijing 102206, P. R. China
| | - Feng-Hua Qi
- School of Information, Beijing Wuzi University, Beijing 101149, P. R. China
| | - Rui Guo
- School of Mathematics, Taiyuan University of Technology, Taiyuan 030024, P. R. China
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Yao YB, Wang XY, Tang B. High-order nonlinear excitations in the Joyeux-Buyukdagli model of DNA. J Biol Phys 2015; 42:213-22. [PMID: 26489740 DOI: 10.1007/s10867-015-9402-3] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/09/2015] [Accepted: 09/14/2015] [Indexed: 11/25/2022] Open
Abstract
By means of the semidiscrete multiple-scale method, we study the existence and properties of high-order envelope solitons and discrete breathers in a homogeneous DNA chain model that is based on pairing enthalpies and site-dependent finite stacking. We obtain the analytical solutions for an envelope soliton, and find that at the Brillouin zone center, discrete breather solutions can appear below the bottom of the phonon band. The behavior of two solitons in collisions and the stability of discrete breathers are confirmed by numerical simulations of the exact equations of the system.
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Affiliation(s)
- Ying-Bo Yao
- College of Communication and Electronic Engineering, Hunan City University, Yiyang, 413000, China
| | - Xiao-Yun Wang
- College of Physics, Mechanical and Electrical Engineering, Jishou University, Jishou, 416000, Hunan, China
| | - Bing Tang
- College of Physics, Mechanical and Electrical Engineering, Jishou University, Jishou, 416000, Hunan, China.
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