On similarity reductions of the three-wave resonant system to the Painleve equations

DOI10.1088/0305-4470/23/15/025zbMath0719.35087OpenAlexW1995480265MaRDI QIDQ5751318

Alexander V. Kitaev

Publication date: 1990

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

Full work available at URL: https://doi.org/10.1088/0305-4470/23/15/025

zbMATH Keywords

Bäcklund transformationPanlevé equations

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53)

Related Items (7)

The sixth Painlevé equation as similarity reduction of \({\widehat{\mathfrak{gl}}_3}\) generalized Drinfel'd-Sokolov hierarchy ⋮ From the Darboux-Egorov system to bi-flat \(F\)-manifolds ⋮ On the linearization of the Painlevé III–VI equations and reductions of the three-wave resonant system ⋮ Necessary conditions for point equivalence of second-order ODEs to the sixth Painlevé equation ⋮ Second harmonic generation: Hamiltonian structures and particular solutions ⋮ Method for Solving the Multidimensional n-Wave Resonant Equations and Geometry of Generalized Darboux-Manakov-Zakharov Systems ⋮ Grothendieck’s dessins d’enfants, their deformations, and algebraic solutions of the sixth Painlevé and Gauss hypergeometric equations

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