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Related papers: Vector NLS solitons interacting with a boundary

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There exist two natural vector generalizations of the completely integrable nonlinear Schr\"odinger (NLS) equation in $1+1$ dimensions: the well-known Manakov model and the lesser-known Kulish-Sklyanin model. In this paper, we propose a…

Exactly Solvable and Integrable Systems · Physics 2015-12-22 Takayuki Tsuchida

In this paper, an extended nonlinear Schrodinger equation with higher-order that includes fifth-order dispersion with matching higher-order nonlinear terms is investigated under zero boundary condition at infinity. Carrying out the spectral…

Exactly Solvable and Integrable Systems · Physics 2020-04-03 Zhou-Zheng Kang , Tie-Cheng Xia

The dynamics of two-component solitons is studied, analytically and numerically, in the framework of a system of coupled extended nonlinear Schr\"odinger equations, which incorporate the cross-phase modulation,…

Pattern Formation and Solitons · Physics 2017-05-19 E. M. Gromov , B. A. Malomed , V. V. Tyutin

Based on recent results obtained by the authors on the inverse scattering method of the vector nonlinear Schr\"odinger equation with integrable boundary conditions, we discuss the factorization of the interactions of N-soliton solutions on…

Mathematical Physics · Physics 2014-05-09 V. Caudrelier , Q. C. Zhang

We consider the linear vector Schr\"odinger equation subjected to quadratic constraints. We demonstrate that the resulting nonlinear system is closely related to the Ablowitz-Ladik hierarchy and use this fact to derive the N-soliton…

Exactly Solvable and Integrable Systems · Physics 2025-10-16 V. E. Vekslerchik

Coupled nonlinear Schrodinger equations (CNLS) with an external elliptic function potential model a quasi one--dimensional interacting two-component Bose-Einstein condensate trapped in a standing light wave. New families of stationary…

Soft Condensed Matter · Physics 2007-05-23 N. A. Kostov , V. Z. Enol'skii , V. S. Gerdjikov , V. V. Konotop , M. Salerno

We consider non-vanishing boundary conditions (NVBC) for the NLS model [6,7,27] in the context of the hybrid dressing transformation and $\tau$-function approach. In order to write the NLS model in a suitable form to deal with non-vanishing…

Exactly Solvable and Integrable Systems · Physics 2009-06-09 L. F. dos Santos , H. Blas , M. J. B. F. da Silva

Physically relevant soliton solutions of the resonant nonlinear Schrodinger (RNLS) equation with nontrivial boundary conditions, recently proposed for description of uniaxial waves in a cold collisionless plasma, are considered in the…

Exactly Solvable and Integrable Systems · Physics 2009-11-11 Jyh-Hao Lee , Oktay K. Pashaev

We analyze the large-$n$ behavior of soliton solutions of the integrable focusing nonlinear Schr\"odinger equation with associated spectral data consisting of a single pair of conjugate poles of order $2n$. Starting from the zero…

Exactly Solvable and Integrable Systems · Physics 2019-05-01 Deniz Bilman , Robert Buckingham

The integrable vector nonlinear Schrodinger (vector NLS) equation is investigated by using Zakharov-Shabat (ZS) scheme. We get a Lax pair formulation of the vector NLS model. Multi-soliton solution of the equation is also derived by using…

solv-int · Physics 2016-09-08 Freddy P. Zen , Hendry I. Elim

Integrable models of resonant interaction of two or more waves in 1+1 dimensions are known to be of applicative interest in several areas. Here we consider a system of three coupled wave equations which includes as special cases the vector…

Exactly Solvable and Integrable Systems · Physics 2015-06-16 Antonio Degasperis , Sara Lombardo

We consider two-component solitons in a medium with a periodic modulation of the nonlinear coefficient. The modulation enables the existence of complex multihump vector states. In particular, vector solitons composed of dipole and…

We investigate non-autonomous solitons in a general coherently coupled nonlinear Schr\"odinger (CCNLS) system with temporally modulated nonlinearities and with an external harmonic oscillator potential. This general CCNLS system encompasses…

Pattern Formation and Solitons · Physics 2020-08-17 R. Babu Mareeswaran , K. Sakkaravarthi , T. Kanna

We present the explicit dark-bright three soliton solution and the associated spectral problem for the variable coefficient integrable coupled NLS equation. Using asymptotic analysis as well as graphical analysis we study the interactions…

Exactly Solvable and Integrable Systems · Physics 2017-12-01 Sudipta Nandy , Abhijit Barthakur

We characterize the soliton solutions of the nonlinear Schroedinger equation on the half line with linearizable boundary conditions. Using an extension of the solution to the whole line and the corresponding symmetries of the scattering…

Exactly Solvable and Integrable Systems · Physics 2015-05-13 Gino Biondini , Guenbo Hwang

We study two integrable systems associated with the coupled NLS equation: the integrable defect system and the integrable boundary systems. Regarding the first one, we present a type I defect condition, which is described by a B\"{a}cklund…

Exactly Solvable and Integrable Systems · Physics 2022-03-01 Baoqiang Xia

We consider a class of multicomponent nonlinear Schrodinger equations (MNLS) related to the symmetric BD.I-type symmetric spaces. As important particular case of these MNLS we obtain the Kulish-Sklyanin model. Some new reductions and their…

Exactly Solvable and Integrable Systems · Physics 2015-05-14 V. S. Gerdjikov

We explore the phenomena of absorption/emission of solitons by an integrable boundary for the nonlinear Schr\"odinger equation on the half-line. This is based on the investigation of time-dependent reflection matrices which satisfy the…

Exactly Solvable and Integrable Systems · Physics 2023-02-01 Vincent Caudrelier , Nicolas Crampe , Eric Ragoucy , Cheng Zhang

Exact analytical soliton solutions play an important role in soliton fields. Soliton solutions were obtained with some special constraints on the nonlinear parameters in nonlinear coupled systems, but they usually do not holds in real…

Pattern Formation and Solitons · Physics 2022-08-12 N. Mao , L. -C. Zhao

Two discretizations of the vector nonlinear Schrodinger (NLS) equation are studied. One of these discretizations, referred to as the symmetric system, is a natural vector extension of the scalar integrable discrete NLS equation. The other…

solv-int · Physics 2009-10-31 M. J. Ablowitz , Y. Ohta , A. D. Trubatch