Soliton scattering with amplitude changes of a negative order AKNS equation

DOI10.1016/j.physd.2009.09.018zbMath1183.37121OpenAlexW1999017987MaRDI QIDQ845038

Jie Ji, Song-Lin Zhao, Da-jun Zhang

Publication date: 5 February 2010

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.physd.2009.09.018

zbMATH Keywords

amplitude\(N\)-soliton solutionsHirota methodnegative order Ablowitz-Kaup-Newell-Sequr (AKNS) equationsoliton scattering

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Soliton equations (35Q51) Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems (37K40)

Related Items (27)

Negative-order KdV equations in (3+1) dimensions by using the KdV recursion operator ⋮ Discrete Analogues of a Negative Order AKNS Equation ⋮ \((2+1)\)-dimensional AKNS \((-N)\) systems. II ⋮ A variety of negative-order integrable KdV equations of higher orders ⋮ Repeated application of the recursion operator for a new hierarchy of negative-order integrable KdV equations ⋮ Solutions and continuum limits to nonlocal discrete sine‐Gordon equations: Bilinearization reduction method ⋮ N -Soliton Solution and Soliton Resonances for the (2+1)-Dimensional Inhomogeneous Gardner Equation ⋮ The Sylvester equation and integrable equations: the Ablowitz-Kaup-Newell-Segur system ⋮ Wave solutions to an integrable negative order KdV equation ⋮ Darboux transformation and general soliton solutions for the reverse space-time nonlocal short pulse equation ⋮ Complex and coupled complex negative order AKNS equation ⋮ Negative-order KdV and negative-order KP equations: multiple soliton solutions ⋮ The integrable Vakhnenko-Parkes (VP) and the modified Vakhnenko-parkes (MVP) equations: multiple real and complex soliton solutions ⋮ The Sylvester equation and the elliptic Korteweg-de Vries system ⋮ Geometric Formulation and Multi‐dark Soliton Solution to the Defocusing Complex Short Pulse Equation ⋮ The generalized Wronskian solutions of a inverse KdV hierarchy ⋮ Multiple complex soliton solutions for integrable negative-order KdV and integrable negative-order modified KdV equations ⋮ Covariant hodograph transformations between nonlocal short pulse models and the AKNS\((- 1)\) system ⋮ Cauchy matrix solutions to some local and nonlocal complex equations ⋮ Solutions of the nonlocal (2+1)-D breaking solitons hierarchy and the negative order AKNS hierarchy ⋮ Binary Darboux transformation for a negative-order AKNS equation ⋮ Negative-order modified KdV equations: multiple soliton and multiple singular soliton solutions ⋮ Negative-order integrable modified KdV equations of higher orders ⋮ Darboux Transformation for a Negative Order AKNS Equation ⋮ [https://portal.mardi4nfdi.de/wiki/Publication:5230893 Hyperelliptic function solutions with finite genus ������ of coupled nonlinear differential equations*] ⋮ A discrete negative AKNS equation: generalized Cauchy matrix approach ⋮ Dark-dark solitons, soliton molecules and elastic collisions in the mixed three-level coupled Maxwell-Bloch equations

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