Links between some \((2 + 1)\)-dimensional nonlinear evolution equations and Painlevé-II equations

DOI10.1016/j.cnsns.2009.02.026zbMath1221.35337OpenAlexW1996802012MaRDI QIDQ718016

Hong-Qing Zhang, Jian-qin Mei, Ding-jiang Huang

Publication date: 23 September 2011

Published in: Communications in Nonlinear Science and Numerical Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cnsns.2009.02.026

zbMATH Keywords

second Painlevé equationBäcklund transformationrational solution\((2 + 1)\)-dimensional nonlinear evolution equations

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Geometric theory, characteristics, transformations in context of PDEs (35A30)

Cites Work

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• A novel class of solutions of the non-stationary Schrödinger and the Kadomtsev-Petviashvili I equations
• Painlevé differential equations in the complex plane
• On the transverse instabilities of solitary waves.
• A connection between nonlinear evolution equations and ordinary differential equations of P-type. I
• A connection between nonlinear evolution equations and ordinary differential equations of P-type. II
• Bäcklund transformations for the second Painlevé hierarchy: a modified truncation approach
• Solutions to the Time Dependent Schrödinger and the Kadomtsev-Petviashvili Equations
• On a unified approach to transformations and elementary solutions of Painlevé equations
• Symmetries and exact solutions of a (2+1)-dimensional sine-Gordon system
• Remarks on the solutions of the Kadomtsev-Petviashvili equation
• Solutions of the first and second Painlevé equations are meromorphic

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