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Research PapersNo Access

THE PAINLEVÉ INTEGRABILITY AND N-SOLITONIC SOLUTION IN TERMS OF THE WRONSKIAN DETERMINANT FOR A VARIABLE-COEFFICIENT VARIANT BOUSSINESQ MODEL OF NONLINEAR WAVES

Ministry-of-Education Key Laboratory of Fluid Mechanics and National Laboratory for Computational Fluid Dynamics, Beijing University of Aeronautics and Astronautics, Beijing 100191, China

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Ministry-of-Education Key Laboratory of Fluid Mechanics and National Laboratory for Computational Fluid Dynamics, Beijing University of Aeronautics and Astronautics, Beijing 100191, China

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

Corresponding author.

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

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

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Ministry-of-Education Key Laboratory of Fluid Mechanics and National Laboratory for Computational Fluid Dynamics, Beijing University of Aeronautics and Astronautics, Beijing 100191, China

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

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Ministry-of-Education Key Laboratory of Fluid Mechanics and National Laboratory for Computational Fluid Dynamics, Beijing University of Aeronautics and Astronautics, Beijing 100191, China

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https://doi.org/10.1142/S0217979209052674Cited by:2 (Source: Crossref)

Abstract

A variable-coefficient variant Boussinesq (VCVB) model describes the propagation of long waves in shallow water, the nonlinear lattice waves, the ion sound waves in plasmas, and the vibrations in a nonlinear string. With the help of symbolic computation, a VCVB model is investigated for its integrability through the Painlevé analysis. Then, by truncating the Painlevé expansion at the constant level term with two singular manifolds, the dependent variable transformations are obtained through which the VCVB model is bilinearized. Furthermore, the corresponding N-solitonic solutions with graphic analysis are given by the Hirota method and Wronskian technique. Additionally, a bilinear Bäcklund transformation is constructed for the VCVB model, by which a sample one-solitonic solution is presented.

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Vol. 23, No. 18

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Received 10 June 2008

Revised 24 July 2008

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