Exact explicit traveling wave solutions for two nonlinear Schrödinger type equations

DOI10.1016/j.amc.2009.06.031zbMath1203.35261OpenAlexW2034042426MaRDI QIDQ609294

Yixiang Geng, Ji-Bin Li, Ji-Xiang Zhang

Publication date: 30 November 2010

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2009.06.031

zbMATH Keywords

solitary wave solutionphase portraitperiodic wave solutionkink and anti-kink wave solutionnonlinear Schrödinger type equations

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Periodic solutions to PDEs (35B10) NLS equations (nonlinear Schrödinger equations) (35Q55) Bifurcation problems for infinite-dimensional Hamiltonian and Lagrangian systems (37K50) Software, source code, etc. for problems pertaining to partial differential equations (35-04) Soliton solutions (35C08)

Related Items (5)

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Uses Software

• Maple

Cites Work

• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Traveling wave solutions for a class of nonlinear dispersive equations
• Orbital stability of solitary waves for the nonlinear derivative Schrödinger equation
• Classification of the solitary waves in coupled nonlinear Schrödinger equations
• Exact travelling wave solutions for the \((n + 1)\)-dimensional double sine- and sinh-Gordon equations
• Explicit and exact travelling wave solutions for the generalized derivative Schrödinger equation
• Extended tanh-function method and reduction of nonlinear Schrödinger-type equations to a quadrature
• Exact solutions for the high-order dispersive cubic-quintic nonlinear Schrödinger equation by the extended hyperbolic auxiliary equation method
• Method for Solving the Korteweg-deVries Equation
• BIFURCATIONS OF TRAVELING WAVE AND BREATHER SOLUTIONS OF A GENERAL CLASS OF NONLINEAR WAVE EQUATIONS
• BIFURCATIONS OF TRAVELING WAVE SOLUTIONS FOR FOUR CLASSES OF NONLINEAR WAVE EQUATIONS
• Symmetries and differential equations
• Smooth and non-smooth traveling waves in a nonlinearly dispersive equation
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