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Research PapersNo Access

ANALYTIC ANALYSIS ON A GENERALIZED (2+1)-DIMENSIONAL VARIABLE-COEFFICIENT KORTEWEG–DE VRIES EQUATION USING SYMBOLIC COMPUTATION

School of Science, P.O. Box 122, Beijing University of Posts and Telecommunications, Beijing 100876, China

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School of Science, P.O. Box 122, Beijing University of Posts and Telecommunications, Beijing 100876, China

State Key Laboratory of Software Development Environment, Beijing University of Aeronautics and Astronautics, Beijing 100191, China

Key Laboratory of Information Photonics and Optical Communications (BUPT), Ministry of Education, Beijing University of Posts and Telecommunications, P.O. Box 128, Beijing 100876, China

Corresponding author.

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School of Science, P.O. Box 122, Beijing University of Posts and Telecommunications, Beijing 100876, China

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School of Science, P.O. Box 122, Beijing University of Posts and Telecommunications, Beijing 100876, China

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https://doi.org/10.1142/S0217979210053975Cited by:1 (Source: Crossref)

Abstract

With the help of symbolic computation, a generalized (2+1)-dimensional variable-coefficient Korteweg–de Vries equation is studied for its Painlevé integrability. Then, Hirota bilinear form is derived, from which the one- and two-solitary-wave solutions with the corresponding graphic illustration are presented. Furthermore, a bilinear auto-Bäcklund transformation is constructed and the nonlinear superposition formula and Lax pair are also obtained. Finally, the analytic solution in the Wronskian form is constructed and proved by direct substitution into the bilinear equation.

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Vol. 24, No. 27

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Received 1 July 2008

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