The Painlevé property, a modified Boussinesq equation and a modified Kadomtsev-Petviashvili equation

DOI10.1016/0167-2789(86)90071-0zbMath0616.35080OpenAlexW2093707152MaRDI QIDQ1821276

Peter A. Clarkson

Publication date: 1986

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0167-2789(86)90071-0

zbMATH Keywords

Boussinesq equationPainlevé propertyKadomtsev-Petviashvili equationcompletely integrable

Mathematics Subject Classification ID

Analyticity in context of PDEs (35A20) Series solutions to PDEs (35C10) Nonlinear higher-order PDEs (35G20) Partial differential equations of mathematical physics and other areas of application (35Q99) Elliptic functions and integrals (33E05)

Related Items (7)

CRE solvability, exact soliton-cnoidal wave interaction solutions, and nonlocal symmetry for the modified Boussinesq equation ⋮ A KdV equation in 2+1 dimensions: Painlevé analysis, solutions and similarity reductions ⋮ The Painlevé-Kowalevski and Poly-Painlevé Tests for Integrability ⋮ Multi-front waves for extended form of modified Kadomtsev-Petviashvili equation ⋮ On invariant solutions of the generalised Boussinesq equation ⋮ Periodic wave solutions and solitary wave solutions of generalized modified Boussinesq equation and evolution relationship between both solutions ⋮ Exact solitary-wave solutions and periodic wave solutions for generalized modified Boussinesq equation and the effect of wave velocity on wave shape

Cites Work

• A boundary value problem associated with the second Painleve transcendent and the Korteweg-de Vries equation
• Nonlinear Evolution Equations Generated from the Backlund Transformation for the Boussinesq Equation
• The Painlevé property for partial differential equations
• The Connection between Partial Differential Equations Soluble by Inverse Scattering and Ordinary Differential Equations of Painlevé Type
• The Painlevé Property and Hirota's Method
• The inverse scattering transform: Semi-infinite interval
• Korteweg-de Vries Equation and Generalizations. I. A Remarkable Explicit Nonlinear Transformation

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