Equivalence transformations in the study of integrability

2014/02/25 by Olena Vaneeva, Olena O Vaneeva, Roman O. Popovych +3 · 3 citations
Physics and Astronomy · Mathematics · #Nonlinear Waves and Solitons #Nonlinear Photonic Systems #Numerical methods for differential equations

paper · doi:10.1088/0031-8949/89/03/038003

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.

Citations

• On the Inverse Scattering Problem for Cubic Eigenvalue Problems of the Class ψxxx + 6Qψx + 6Rψ = λψ

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• Application of Lie-group symmetry analysis to an infinite hierarchy of differential equations at the example of first order ODEs

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