Equivalence transformations in the study of integrability

2013/08/31 by Olena O Vaneeva, Olena Vaneeva, Olena O. Vaneeva +4 · 49 citations
Mathematics · Physics and Astronomy · #Applied mathematics #Class (philosophy) #Computer science #Differential algebraic equation #Differential equation #Equivalence (formal languages) #Equivalence class (music) #Equivalence relation #Integrable system #Korteweg–de Vries equation #Mathematical analysis #Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Nonlinear system #Numerical methods for differential equations #Ordinary differential equation #Physics #Pure mathematics #Variable (mathematics) #Variable coefficient #math-ph #math.MP #msc:35Q53 #msc:37K10 #msc:37K35 #nlin.SI

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

published in Physica Scripta 89(3), 038003 (IOP Publishing) · 14 pages; the version accepted to Physica Scripta

arxiv created 2013/11/25 · openalex publication_date 2014/02/25 · arxiv updated 2014/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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

Cited by

• Extended group analysis and conservation laws of a class of variable coefficient generalized Kawahara equations
• Painlevé Integrability And Shifted Nonlocal Reductions Of A Variable Coefficient Coupled HI Mkdv System
• Application of Lie-group symmetry analysis to an infinite hierarchy of differential equations at the example of first order ODEs
• Group analysis of variable coefficient generalized fifth-order KdV equations
• Symmetries of 2+1-dimensional variable coefficient Burgers equations
• Dispersionless (3+1)-dimensional integrable hierarchies. [europepmc]

Related

• Equivalence groupoid of a class of variable coefficient Korteweg–de Vries equations
• Equivalence for Differential Equations
• Classification of Integrable Evolution Equations of the Form u_t=u_xxx+f(t,x,u,u_x,u_xx)
• On dummy variables of structure-preserving transformations
• Equivalence and integrability of second order linear ODEs