Equivalence transformations in the study of integrability

Abstract

We discuss how point transformations can be used for the study of integrability, in particular, for deriving classes of integrable variable-coefficient differential equations. The procedure of finding the equivalence groupoid of a class of differential equations is described and then specified for the case of evolution equations. A class of fifth-order variable-coefficient KdV-like equations is studied within the framework suggested.

14 pages; the version accepted to Physica Scripta

References in corpus (3)

• Enhanced Group Analysis and Exact Solutions of Variable Coefficient Semilinear Diffusion Equations with a Power Source
• Nonisospectral integrable nonlinear equations with external potentials and their GBDT solutions
• Bäcklund-Darboux Transformation for Non-Isospectral Canonical System and Riemann-Hilbert Problem

Cited by in corpus (17)

• A Simple Construction of Recursion Operators for Multidimensional Dispersionless Integrable Systems
• Numerical solutions of boundary value problems for variable coefficient generalized KdV equations using Lie symmetries
• Group classification of linear evolution equations
• Group analysis of general Burgers-Korteweg-de Vries equations
• Extended symmetry analysis of generalized Burgers equations
• Symmetries and conservation laws for the Karczewska--Rozmej--Rutkowski--Infeld equation
• Equivalence groupoid of a class of variable coefficient Korteweg--de Vries equations
• Equivalence groupoid and group classification of a class of variable-coefficient Burgers equations
• Equivalence groupoids of classes of linear ordinary differential equations and their group classification
• Classification of reduction operators and exact solutions of variable coefficient Newell-Whitehead-Segel equations
• Dispersionless (3+1)-dimensional integrable hierarchies
• Integrable (3+1)-dimensional system with an algebraic Lax pair
• Application of Lie-group symmetry analysis to an infinite hierarchy of differential equations at the example of first order ODEs
• Symmetry reductions of a generalized Kuramoto-Sivashinsky equation via equivalence transformations
• Group analysis of variable coefficient generalized fifth-order KdV equations
• Lie symmetries of a generalized Kuznetsov-Zabolotskaya-Khoklov equation
• Symmetries of 2+1-dimensional variable coefficient Burgers equations