Symmetry classification of the Gardner equation with time-dependent coefficients arising in stratified fluids

DOI10.1016/j.cnsns.2011.09.002zbMath1245.35110OpenAlexW2045979957MaRDI QIDQ430454

M. P. Ramollo, Motlatsi Molati

Publication date: 21 June 2012

Published in: Communications in Nonlinear Science and Numerical Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cnsns.2011.09.002

zbMATH Keywords

similarity solutionsgroup classificationGardner equation

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) KdV equations (Korteweg-de Vries equations) (35Q53) Symmetries, invariants, etc. in context of PDEs (35B06)

Related Items (12)

Some Solutions of Generalised Variable Coefficients KdV Equation by Classical Lie Approach ⋮ Differential invariants of a generalized variable-coefficient Gardner equation ⋮ Lie symmetry analysis of the time-variable coefficient B-BBM equation ⋮ On the classical and nonclassical symmetries of a generalized Gardner equation ⋮ Equivalence transformations and conservation laws for a generalized variable-coefficient Gardner equation ⋮ Enhanced group classification of gardner equations with time-dependent coefficients ⋮ On Lie symmetries and invariant solutions of (2+1)-dimensional Gardner equation ⋮ Symmetry reductions of a generalized Kuramoto-Sivashinsky equation via equivalence transformations ⋮ An Overview of the Generalized Gardner Equation: Symmetry Groups and Conservation Laws ⋮ Symmetry classification and invariant solutions of the variable coefficient BBM equation ⋮ Lie group analysis of a forced KdV equation ⋮ On symmetries and conservation laws of a Gardner equation involving arbitrary functions

Uses Software

• YaLie

Cites Work

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• A study on KdV and Gardner equations with time-dependent coefficients and forcing terms
• Lie group classification and invariant solutions of mKdV equation with time-dependent coefficients
• More common errors in finding exact solutions of nonlinear differential equations. I
• Time-dependent symmetries of variable-coefficient evolution equations and graded Lie algebras
• Graded Symmetry Algebras of Time-Dependent Evolution Equations and Application to the Modified KP Equations
• Symmetries and differential equations

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