Auto-Bäcklund transformations and integrability of ordinary and partial differential equations

DOI10.1063/1.3321637zbMath1309.34145OpenAlexW2088064134MaRDI QIDQ5246625

Juan M. Conde, Andrew Pickering, Pilar Ruiz Gordoa

Publication date: 21 April 2015

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.3321637

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35)

Related Items (6)

A special solution technique: further extensions ⋮ A new kind of Bäcklund transformation for partial differential equations ⋮ Exact solutions of a novel integrable partial differential equation ⋮ Bäcklund transformation of matrix equations and a discrete matrix first Painlevé equation ⋮ Auto-Bäcklund transformations for a matrix partial differential equation ⋮ Bäcklund transformations for new fourth Painlevé hierarchies

Cites Work

• KdV6: an integrable system
• Integration via modification: a method of reduction of order for systems of ordinary differential equations
• Painlevé hierarchies and the Painlevé test
• A method of reduction of order for discrete systems
• Bäcklund transformations for a discrete second Painlevé hierarchy
• Evolution equations possessing infinitely many symmetries
• The Inverse Scattering Transform‐Fourier Analysis for Nonlinear Problems
• Nonisospectral scattering problems: A key to integrable hierarchies
• The singular manifold method revisited
• A new integrable generalization of the Korteweg–de Vries equation

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