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Multi-soliton solutions, breather-like and bound-state solitons for complex modified Korteweg–de Vries equation in optical fibers
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作者 兰中周 《Chinese Physics B》 SCIE EI CAS CSCD 2024年第6期119-123,共5页
Under investigation in this paper is a complex modified Korteweg–de Vries(KdV) equation, which describes the propagation of short pulses in optical fibers. Bilinear forms and multi-soliton solutions are obtained thro... Under investigation in this paper is a complex modified Korteweg–de Vries(KdV) equation, which describes the propagation of short pulses in optical fibers. Bilinear forms and multi-soliton solutions are obtained through the Hirota method and symbolic computation. Breather-like and bound-state solitons are constructed in which the signs of the imaginary parts of the complex wave numbers and the initial separations of the two parallel solitons are important factors for the interaction patterns. The periodic structures and position-induced phase shift of some solutions are introduced. 展开更多
关键词 complex modified KdV equation multi-soliton solutions breather-like BOUND-STATE
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Cross-kink multi-soliton solutions for the (3+1)-D Jimbo-Miwa equation
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作者 Zhenhui Xu Hanlin Chen 《Open Journal of Applied Sciences》 2012年第4期215-218,共4页
In this paper, by using bilinear form and extended three-wave type of ans¨atz approach, we obtain new cross-kink multi-soliton solutions of the (3+1)-dimensional Jimbo-Miwa equation, including the periodic breath... In this paper, by using bilinear form and extended three-wave type of ans¨atz approach, we obtain new cross-kink multi-soliton solutions of the (3+1)-dimensional Jimbo-Miwa equation, including the periodic breather-type of kink three-soliton solutions, the cross-kink four-soliton solutions, the doubly periodic breathertype of soliton solutions and the doubly periodic breather-type of cross-kink two-soliton solutions. It is shown that the generalized three-wave method, with the help of symbolic computation, provides an effective and powerful mathematical tool for solving high dimensional nonlinear evolution equations in mathematical physics. 展开更多
关键词 Jimbo-Miwa EQUATION EXTENDED three-wave method cross-kink multi-soliton.
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Multi-soliton solutions for the coupled modified nonlinear Schrdinger equations via Riemann–Hilbert approach 被引量:3
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作者 Zhou-Zheng Kang Tie-Cheng Xia Xi Ma 《Chinese Physics B》 SCIE EI CAS CSCD 2018年第7期171-178,共8页
The coupled modified nonlinear Schrodinger equations are under investigation in this work. Starting from analyzing the spectral problem of the Lax pair, a Riemann-Hilbert problem for the coupled modified nonlinear Sch... The coupled modified nonlinear Schrodinger equations are under investigation in this work. Starting from analyzing the spectral problem of the Lax pair, a Riemann-Hilbert problem for the coupled modified nonlinear Schrodinger equations is formulated. And then, through solving the obtained Riemann-Hilbert problem under the conditions of irregularity and reflectionless case, N-soliton solutions for the equations are presented. Furthermore, the localized structures and dynamic behaviors of the one-soliton solution are shown graphically. 展开更多
关键词 coupled modified nonlinear Schrodinger equations Riemann-Hilbert approach multi-soliton so-lutions
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Head-on collision between single-and multi-soliton heavy ion acoustic waves in multi-ion plasmas
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作者 M S ALAM M R TALUKDER 《Plasma Science and Technology》 SCIE EI CAS CSCD 2019年第9期58-72,共15页
Head-on collisions among the single-and multi-soliton’s heavy ion acoustic waves(HIAWs) of multi-ion plasma are studied. The plasma consists of adiabatic positively charged inertial heavy ions, Boltzmann energy distr... Head-on collisions among the single-and multi-soliton’s heavy ion acoustic waves(HIAWs) of multi-ion plasma are studied. The plasma consists of adiabatic positively charged inertial heavy ions, Boltzmann energy distributed light ions and kappa energy distributed electrons. The extended poincaré-Lighthill-Kuo(e PLK) method is applied for the derivation of two-sided Korteweg–de Vries(KdV) equations(KdVEs). The KdV single-soliton solutions(KdVSSs) are determined using the hyperbolic secant method and the KdV multi-soliton solutions(KdVMSs)are obtained using the Hirota method. The effects of superthermality of electrons, temperature ratios of electron to light ion and heavy ion to electron, and the density ratio of electron to heavy ion on phase shifts are investigated for the head-on collisions between two-soliton HIAWs. The effects of plasma parameters on angular frequency, phase speed, production of multi-soliton structures, and the head-on collisions among single-, double-, triple-, quadruple-, and quintuplesolitons are also studied. 展开更多
关键词 HIAWs multi-soliton kappa-distribution ePLK METHOD Hirotta's METHOD multi-ion
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Multi-Waves,Breathers,Periodic and Cross-Kink Solutions to the(2+1)-Dimensional Variable-Coefficient Caudrey-Dodd-Gibbon-Kotera-Sawada Equation
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作者 LIU Dong JU Xiaodong +2 位作者 ILHAN Onur Alp MANAFIAN Jalil ISMAEL Hajar Farhan 《Journal of Ocean University of China》 SCIE CAS CSCD 2021年第1期35-44,共10页
The present article deals with multi-waves and breathers solution of the(2+1)-dimensional variable-coefficient CaudreyDodd-Gibbon-Kotera-Sawada equation under the Hirota bilinear operator method.The obtained solutions... The present article deals with multi-waves and breathers solution of the(2+1)-dimensional variable-coefficient CaudreyDodd-Gibbon-Kotera-Sawada equation under the Hirota bilinear operator method.The obtained solutions for solving the current equation represent some localized waves including soliton,solitary wave solutions,periodic and cross-kink solutions in which have been investigated by the approach of the bilinear method.Mainly,by choosing specific parameter constraints in the multi-waves and breathers,all cases the periodic and cross-kink solutions can be captured from the 1-and 2-soliton.The obtained solutions are extended with numerical simulation to analyze graphically,which results in 1-and 2-soliton solutions and also periodic and cross-kink solutions profiles.That will be extensively used to report many attractive physical phenomena in the fields of acoustics,heat transfer,fluid dynamics,classical mechanics,and so on.We have shown that the assigned method is further general,efficient,straightforward,and powerful and can be exerted to establish exact solutions of diverse kinds of fractional equations originated in mathematical physics and engineering.We have depicted the figures of the evaluated solutions in order to interpret the physical phenomena. 展开更多
关键词 variable-coefficient Caudrey-Dodd-Gibbon-Kotera-Sawada equation Hirota bilinear operator method soliton multi-waves and breathers periodic and cross-kink solitray wave solutions
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Diverse soliton solutions and dynamical analysis of the discrete coupled mKdV equation with 4×4 Lax pair
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作者 刘雪珂 闻小永 《Chinese Physics B》 SCIE EI CAS CSCD 2023年第12期179-191,共13页
Under consideration in this study is the discrete coupled modified Korteweg-de Vries(mKdV)equation with 4×4 Lax pair.Firstly,through using continuous limit technique,this discrete equation can be mapped to the co... Under consideration in this study is the discrete coupled modified Korteweg-de Vries(mKdV)equation with 4×4 Lax pair.Firstly,through using continuous limit technique,this discrete equation can be mapped to the coupled KdV and mKdV equations,which may depict the development of shallow water waves,the optical soliton propagation in cubic nonlinear media and the Alfven wave in a cold collision-free plasma.Secondly,the discrete generalized(r,N-r)-fold Darboux transformation is constructed and extended to solve this discrete coupled equation with the fourth-order linear spectral problem,from which diverse exact solutions including usual multi-soliton and semi-rational soliton solutions on the vanishing background,higher-order rational soliton and mixed hyperbolic-rational soliton solutions on the non-vanishing background are derived,and the limit states of some soliton and rational soliton solutions are analyzed by the asymptotic analysis technique.Finally,the numerical simulations are used to explore the dynamical behaviors of some exact soliton solutions.These results may be helpful for understanding some physical phenomena in fields of shallow water wave,optics,and plasma physics. 展开更多
关键词 discrete coupled mKdV equation continuous limit discrete generalized(r N-r)-fold Darboux transformation multi-soliton solutions rational soliton solutions
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Darboux Transformation and Solitons for Reduced Maxwell-Bloch Equations
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作者 JIQing-Chun 《Communications in Theoretical Physics》 SCIE CAS CSCD 2005年第6期983-986,共4页
The Darboux transformations from arbitrary solutions of reduced Maxwell-Bloch equations is constructed in this article. Hence, in principle, we can find multi-soliton solutions by algebric algorithm, and the formula w... The Darboux transformations from arbitrary solutions of reduced Maxwell-Bloch equations is constructed in this article. Hence, in principle, we can find multi-soliton solutions by algebric algorithm, and the formula will be given explicitly. 展开更多
关键词 reduced Maxwell-Bloch equations Lax pair Darboux transformations SOLITONS multi-solitons
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N-Fold Darboux Transformation and Bidirectional Solitons for Whitham-Broer-Kaup Model in Shallow Water
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作者 王雷 高以天 +3 位作者 盖晓玲 孟得新 吕兴 于鑫 《Communications in Theoretical Physics》 SCIE CAS CSCD 2010年第3期413-422,共10页
Under investigation in this paper is the Whitham-Broer-Kaup (WBK) system, which describes the dispersive long wave in shallow water. Through a variable transformation, the WBK system is casted into a general Broer-Kau... Under investigation in this paper is the Whitham-Broer-Kaup (WBK) system, which describes the dispersive long wave in shallow water. Through a variable transformation, the WBK system is casted into a general Broer-Kaup system whose Lax pair can be derived by the Ablowitz-Kaup-Newell-Segur technology. With symbolic computation, based on the aforementioned Lax pair, the N-fold Darboux transformation is constructed with a gauge transformation and the multi-soliton solutions are obtained. Finally, the elastic interactions of the two-soliton solutions (including the head-on and overtaking collisions) for the WBK system are graphically studied. Those multi-soliton collisions can beused to illustrate the bidirectional propagation of the waves in shallow water. 展开更多
关键词 Whitham Broer-Kaup system Bidirectional solitons multi-soliton solutions N-fold Darboux transformation Lax pair
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Nonautonomous bright solitons and soliton collisions in a nonlinear medium with an external potential
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作者 李画眉 葛龙 何俊荣 《Chinese Physics B》 SCIE EI CAS CSCD 2012年第5期145-152,共8页
We present exact bright multi-soliton solutions of a generalized nonautonomous nonlinear Schroinger equation with time-and space-dependent distributed coefficients and an external potential which describes a pulse pro... We present exact bright multi-soliton solutions of a generalized nonautonomous nonlinear Schroinger equation with time-and space-dependent distributed coefficients and an external potential which describes a pulse propagating in nonlinear media when its transverse and longitudinal directions are nonuniformly distributed.Such solutions exist in certain constraint conditions on the coefficients depicting dispersion,nonlinearity,and gain(loss).Various shapes of bright solitons and interesting interactions between two solitons are observed.Physical applications of interest to the field and stability of the solitons are discussed. 展开更多
关键词 generalized nonautonomous nonlinear Schrodinger equation multi-soliton solution Fourier-synthesized optical lattice potential flying bird potential
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Soliton interactions and asymptotic state analysis in a discrete nonlocal nonlinear self-dual network equation of reverse-space type
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作者 Cui-Lian Yuan Xiao-Yong Wen 《Chinese Physics B》 SCIE EI CAS CSCD 2021年第3期105-118,共14页
We propose a reverse-space nonlocal nonlinear self-dual network equation under special symmetry reduction,which may have potential applications in electric circuits.Nonlocal infinitely many conservation laws are const... We propose a reverse-space nonlocal nonlinear self-dual network equation under special symmetry reduction,which may have potential applications in electric circuits.Nonlocal infinitely many conservation laws are constructed based on its Lax pair.Nonlocal discrete generalized(m,N−m)-fold Darboux transformation is extended and applied to solve this system.As an application of the method,we obtain multi-soliton solutions in zero seed background via the nonlocal discrete N-fold Darboux transformation and rational solutions from nonzero-seed background via the nonlocal discrete generalized(1,N−1)-fold Darboux transformation,respectively.By using the asymptotic and graphic analysis,structures of one-,two-,three-and four-soliton solutions are shown and discussed graphically.We find that single component field in this nonlocal system displays unstable soliton structure whereas the combined potential terms exhibit stable soliton structures.It is shown that the soliton structures are quite different between discrete local and nonlocal systems.Results given in this paper may be helpful for understanding the electrical signals propagation. 展开更多
关键词 reverse-space nonlocal nonlinear self-dual network equation nonlocal discrete generalized(m N−m)-fold Darboux transformation multi-soliton solutions rational solutions
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The multi-soliton solutions of the CH-γ equation 被引量:3
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作者 CHEN ChunLi~(1+) LI YiShen~2 ZHANG JinE~3 1 Department of Mathematics,Shanghai Jiaotong University,Shanghai 200240,China 2 Department of Mathematics,University of Science and Technology of China,Hefei 230026,China 3 SB and SEF,University of Hong Kong,Pokfulam Road,Hong Kong,China 《Science China Mathematics》 SCIE 2008年第2期314-320,共7页
This paper solves the integrable CH-γequation for analytical multiple soliton solutions with the Darboux transformation method.Some properties of the soliton solutions are different from the CH equation.
关键词 CH-γ equation multi-soliton solutions Darboux transformation 35Q35 35Q51
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Multi-soliton fusion phenomenon of Burgers equation and fission, fusion phenomenon of Sharma-Tasso-Olver equation 被引量:5
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作者 Harun Or-Roshid M.M.Rashidi 《Journal of Ocean Engineering and Science》 SCIE 2017年第2期120-126,共7页
A direct rational exponential scheme is proposed to construct exact multi-soliton solutions and its fission,fusion phenomena after interaction of the solitons has been discussed.We have considered the Burgers and Shar... A direct rational exponential scheme is proposed to construct exact multi-soliton solutions and its fission,fusion phenomena after interaction of the solitons has been discussed.We have considered the Burgers and Sharma-Tasso-Olver equation as two concrete examples to show the fission and fusion of the solitary wave and the solitons,respectively.We improve different structured multi-soliton solutions with possible conditions for fission and fusion of the Burgers and the Sharma-Tasso-Olver equations arises in plasma physics and in ocean dynamics.The amplitude and velocity relations between solitons and/or solitary waves before and after interactions are given and a possible condition for fission and fusion is proposed.Furthermore,three-dimensional plots of the wave solutions are given to visualize the dynamics of the model.©2017 Shanghai Jiaotong University.Published by Elsevier B.V. 展开更多
关键词 Direct rational exponential scheme Burger equation Sharma-Tasso-Olver equation Traveling wave solutions multi-soliton
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Exact chirped multi-soliton solutions of the nonlinear Schr(o|¨)dinger equation with varying coefficients 被引量:5
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作者 郝瑞宇 李录 +2 位作者 杨荣草 李仲豪 周国生 《Chinese Optics Letters》 SCIE EI CAS CSCD 2005年第3期136-139,共4页
In this letter, exact chirped multi-soliton solutions of the nonlinear Schrodinger (NLS) equation with varying coefficients are found. The explicit chirped one- and two-soliton solutions are generated. As an example, ... In this letter, exact chirped multi-soliton solutions of the nonlinear Schrodinger (NLS) equation with varying coefficients are found. The explicit chirped one- and two-soliton solutions are generated. As an example, an exponential distributed control system is considered, and some main features of solutions are shown. The results reveal that chirped soliton can all be nonlinearly compressed cleanly and efficiently in an optical fiber with no loss or gain, with the loss, or with the gain. Furthermore, under the same initial condition, compression of optical soliton in the optical fiber with the loss is the most dramatic. Also, under nonintegrable condition and finite initial perturbations, the evolution of chirped soliton has been demonstrated by simulating numerically. 展开更多
关键词 Exact chirped multi-soliton solutions of the nonlinear Schr dinger equation with varying coefficients
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Multi-solitons for a generalized Davey-Stewartson system
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作者 WANG Zhong CUI ShangBin 《Science China Mathematics》 SCIE CSCD 2017年第4期651-670,共20页
This paper studies multi-solitons of non-integrable generalized Davey-Stewartson system in the elliptic-elliptic case. By extending the method for constructing multi-solitons of non-integrable nonlinear SchrSdinger eq... This paper studies multi-solitons of non-integrable generalized Davey-Stewartson system in the elliptic-elliptic case. By extending the method for constructing multi-solitons of non-integrable nonlinear SchrSdinger equations and systems developed by Martel et al. to the present non-integrable generalized Davey- Stewartson system and overcoming some new difficulties caused by the nonlocal operator B, we prove the existence of multi-solitons for this system. Furthermore, we also give a generalization of this result to a more general class of equations with nonlocal nonlinearities. 展开更多
关键词 Davey-Stewartson system multi-solitons EXISTENCE NONLOCAL
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Multi-soliton solutions of a two-component Camassa–Holm system:Darboux transformation approach
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作者 Gaihua Wang Nianhua Li Q P Liu 《Communications in Theoretical Physics》 SCIE CAS CSCD 2020年第4期23-28,共6页
We propose and develop another approach to constructing multi-soliton solutions of an integrable two-component Camassa–Holm(CH2)system.With the help of a reciprocal transformation and a gauge transformation,we relate... We propose and develop another approach to constructing multi-soliton solutions of an integrable two-component Camassa–Holm(CH2)system.With the help of a reciprocal transformation and a gauge transformation,we relate the CH2 system to a negative flow of the Broer–Kaup or twoboson hierarchy.The solutions of this negative flow are given in terms of Wronskians via Darboux transformation.Then the multi-soliton solutions of the CH2 system are recovered in parametric form by inverting the reciprocal transformation and the gauge transformation. 展开更多
关键词 DARBOUX TRANSFORMATION reciprocal TRANSFORMATION TWO-COMPONENT Camassa–Holm system multi-soliton SOLUTIONS
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Multi-Soliton Solutions and Integrable Discretization for a Coupled Modified Volterra Lattice Equation
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作者 赵海琼 朱佐农 《Communications in Theoretical Physics》 SCIE CAS CSCD 2012年第8期244-250,共7页
In this paper, we study a coupled modified Volterra lattice equation which is an integrable semidiscrete version of the coupled KdV and the coupled mKdV equation. By using the Darboux transformation, we obtain its new... In this paper, we study a coupled modified Volterra lattice equation which is an integrable semidiscrete version of the coupled KdV and the coupled mKdV equation. By using the Darboux transformation, we obtain its new explicit solutions including multi-soliton and multi-positon. Furthermore, an integrable discretization of the coupled modified Volterra lattice equation is constructed. 展开更多
关键词 coupled modified Volterra lattice multi-soliton integrable discretization
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Investigation of Multi-soliton,Multi-cuspon Solutions to the Camassa-Holm Equation and Their Interaction
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作者 Xiaozhou LI Yan XU Yishen LI 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2012年第2期225-246,共22页
The authors study the multi-soliton, multi-cuspon solutions to the Camassa- Holm equation and their interaction. According to the solution formula due to Li in 2004 and 2005, the authors give the proper choice of para... The authors study the multi-soliton, multi-cuspon solutions to the Camassa- Holm equation and their interaction. According to the solution formula due to Li in 2004 and 2005, the authors give the proper choice of parameters for multi-soliton and multicuspon solutions, especially for n ≥ 3 case. The numerical method (the so-called local discontinuous Galerkin (LDG) method) is also used to simulate the solutions and give the comparison of exact solutions and numerical solutions. The numerical results for the two-soliton and one-cuspon, one-soliton and two-cuspon, three-soliton, three-cuspon, three-soliton and one-cuspon, two-soliton and two-cuspon, one-soliton and three-cuspon, four-soliton and four-cuspon are investigated respectively. by the numerical method for the first time 展开更多
关键词 Camassa-Holm equation Local discontinuous Galerkin method multi-soliton Multi-cuspon
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Multi-soliton solutions for the three types of nonlocal Hirota equations via Riemann-Hilbert approach
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作者 Yindong Zhuang Yi Zhang +1 位作者 Heyan Zhang Pei Xia 《Communications in Theoretical Physics》 SCIE CAS CSCD 2022年第11期37-44,共8页
The purpose of the paper is to formulate multi-soliton solutions for the nonlocal Hirota equations via the Riemann-Hilbert(RH)approach.The RH problems are constructed and the zero structures are studied via performing... The purpose of the paper is to formulate multi-soliton solutions for the nonlocal Hirota equations via the Riemann-Hilbert(RH)approach.The RH problems are constructed and the zero structures are studied via performing spectral analysis of the Lax pair.Then we consider three types of nonlocal Hirota equations by discussing different symmetry reductions of the potential matrix.On the basis of the resulting matrix RH problem under the restriction of the reflectionless case,we successfully obtain the multi-soliton solutions of the nonlocal Hirota equations. 展开更多
关键词 the nonlocal Hirota equation Riemann-Hilbert approach multi-soliton solutions
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Bounded multi-soliton solutions and their asymptotic analysis for the reversal-time nonlocal nonlinear Schrodinger equation
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作者 Wei-Jing Tang Zhang-nan Hu Liming Ling 《Communications in Theoretical Physics》 SCIE CAS CSCD 2021年第10期1-13,共13页
In this paper, we construct the Darboux transformation(DT) for the reverse-time integrable nonlocal nonlinear Schrodinger equation by loop group method. Then we utilize the DT to derive soliton solutions with zero see... In this paper, we construct the Darboux transformation(DT) for the reverse-time integrable nonlocal nonlinear Schrodinger equation by loop group method. Then we utilize the DT to derive soliton solutions with zero seed. We investigate the dynamical properties for those solutions and present a sufficient condition for the non-singularity of multi-soliton solutions.Furthermore, the asymptotic analysis of bounded multi-solutions has also been established by the determinant formula. 展开更多
关键词 nonlocal nonlinear Schrodinger equation multi-soliton solution SINGULARITY asymptotic analysis
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multi-solitons interaction multicomponent plasma extended Poincare–Lighthill–Kuo method head-on collision
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作者 Kaushik Roy Malay Kumar Ghorui +1 位作者 Prasanta Chatterjee Mouloud Tribeche 《Communications in Theoretical Physics》 SCIE CAS CSCD 2016年第2期237-246,共10页
The propagation and interaction between ion acoustic multi-solitons in an unmagnetized multicomponent plasma consisting of fluid hot ions, positrons and both hot and cold electrons, are investigated by employing the e... The propagation and interaction between ion acoustic multi-solitons in an unmagnetized multicomponent plasma consisting of fluid hot ions, positrons and both hot and cold electrons, are investigated by employing the extended Poincare–Lighthill–Kuo(PLK) method. Two different Kortewege-de Vries(K-dV) equations are derived. The Hirota's method is applied to get the K-dV multi-solitons solution. The phase shift due to the overtaking and head- on collision of the multi-solitons is obtained. 展开更多
关键词 Head-on Collision of Ion-acoustic multi-solitons in e-p-i Plasma
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