Lax pairs, Backlund transformations and special solutions for ordinary differential equations

DOI10.1088/0951-7715/1/3/005zbMath0682.34011OpenAlexW1984838555MaRDI QIDQ4731480

Yunbo Zeng, Alan C. Newell, M. Tabors, John D. Gibbon

Publication date: 1988

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1088/0951-7715/1/3/005

zbMATH Keywords

ordinary differential equationsBäcklund transformationsKorteweg-de Vries equationLax pairssecond Painlevé transcendenttravelling wave reductionspecial solutionsfourth Painlevé transcendentsWeiss-Tabor-Carnevale procedure

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Partial differential equations of mathematical physics and other areas of application (35Q99)

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Linearity inside nonlinearity: Exact solutions to the complex Ginzburg-Landau equation ⋮ The Painlevé-Kowalevski and Poly-Painlevé Tests for Integrability ⋮ New symmetry reductions and exact solutions of the Davey–Stewartson system. I. Reductions to ordinary differential equations ⋮ Painlevé expansion and exact solution for nonlinear evolution equations ⋮ A Truncation for Obtaining all the First Degree Birational Transformations of the Painlevé Transcendents ⋮ Bäcklund Transformations and Solution Hierarchies for the Fourth Painlevé Equation ⋮ The Bäcklund transformations and abundant exact explicit solutions for a general nonintegrable nonlinear convection-diffusion equation ⋮ Similarity reductions from extended Painlevé expansions for nonintegrable evolution equations ⋮ New exact solutions of the Boussinesq equation ⋮ A Multidimensional Superposition Principle: Classical Solitons IV ⋮ Nonclassical symmetry reductions of the Boussinesq equation ⋮ Nonclassical symmetry reductions of nonlinear partial differential equations

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