The direct symmetry method and its application in variable coefficients Schrödinger equation

DOI10.1016/J.AMC.2006.08.084zbMath1119.35362OpenAlexW2089568901MaRDI QIDQ883867

Zhi-Lian Yan, Ling Wang, Xi-Qiang Liu

Publication date: 12 June 2007

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

Full work available at URL: https://doi.org/10.1016/j.amc.2006.08.084

zbMATH Keywords

similarity solutionsymmetry reduction

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures (37K30)

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A simple direct method to find equivalence transformations of a generalized nonlinear Schrödinger equation and a generalized KdV equation ⋮ Explicit solutions of the (2 + 1)-dimensional AKNS shallow water wave equation with variable coefficients ⋮ New exact solutions to the compound KdV-Burgers system with nonlinear terms of any order ⋮ Symmetry reductions and similarity solutions of the \((3+1)\)-dimensional breaking soliton equation ⋮ Optimal system, group invariant solutions and conservation laws of the CGKP equation ⋮ A generalized (\(G{^{\prime}}/G\))-expansion method and its applications to nonlinear evolution equations

Cites Work

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• Similarity solutions to non-linear partial differential equation of physical phenomena represented by the Zakharov-Kuznetsov equation
• Symmetry and similarity solutions of variable coefficients generalized Zakharov-Kuznetsov equation
• Soliton solutions in linear magnetic field and time-dependent laser field.
• Symmetry Reductions and Explicit Solutions for a Generalized Zakharov–Kuznetsov Equation
• Slowly varying solitary waves. II. Nonlinear Schrödinger equation
• Painlevé analysis of the damped, driven nonlinear Schrödinger equation
• Group-invariant solutions of the (2+1)-dimensional cubic Schrödinger equation

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