Soliton, rational and special solutions of the Korteweg-de Vries hierarchy

DOI10.1016/j.amc.2009.11.024zbMath1203.35229OpenAlexW1975826384MaRDI QIDQ609343

Nikolay A. Kudryashov

Publication date: 30 November 2010

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2009.11.024

zbMATH Keywords

self-similar solutionssolitonrational solutionsKorteweg-de Vries equationnonlinear evolution equationKorteweg-de Vries hierarchyfirst Painlevé hierarchysecond Painlevé hierarchy

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) KdV equations (Korteweg-de Vries equations) (35Q53) Soliton equations (35Q51) Soliton solutions (35C08) Polynomial solutions to PDEs (35C11)

Related Items (6)

Lax pairs and special polynomials associated with self-similar reductions of Sawada -- Kotera and Kupershmidt equations ⋮ Higher Painlevé transcendents as special solutions of some nonlinear integrable hierarchies ⋮ On integrability and quasi-periodic wave solutions to a \((3+1)\)-dimensional generalized KdV-like model equation ⋮ Rational and special solutions for some Painlevé hierarchies ⋮ Lax pair and first integrals of the traveling wave reduction for the KdV hierarchy ⋮ Lax pairs and rational solutions of similarity reductions for Kupershmidt and Sawada-Kotera hierarchies

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