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DOE OSTI · 21567430

Integrability study on a generalized (2+1)-dimensional variable-coefficient Gardner model with symbolic computation

Xing, Lue·Haiqiang, Zhang·Tao, Xu·He, Li·Bo, Tian
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Abstract

Gardner model describes certain nonlinear elastic structures, ion-acoustic waves in plasmas, and shear flows in ocean and atmosphere. In this paper, by virtue of the computerized symbolic computation, the integrability of a generalized (2+1)-dimensional variable-coefficient Gardner model is investigated. Painleve integrability conditions are derived among the coefficient functions, which reduce all the coefficient functions to be proportional only to {gamma}(t), the coefficient of the cubic nonlinear term u{sup 2}u{sub x}. Then, an independent transformation of the variable t transforms the reduced {gamma}(t)-dependent equation into a constant-coefficient integrable one. Painleve test shows that this is the only case when our original generalized (2+1)-dimensional variable-coefficient Gardner model is integrable.

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71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICSCALCULATION METHODSDIFFERENTIAL EQUATIONSEQUATIONSINTEGRAL CALCULUSION ACOUSTIC WAVESION WAVESMATHEMATICSNONLINEAR PROBLEMSONE-DIMENSIONAL CALCULATIONSPARTIAL DIFFERENTIAL EQUATIONSPLASMAPLASMA WAVESSHEARTRANSFORMATIONSWAVE EQUATIONS

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Xing, Lue, Haiqiang, Zhang, Tao, Xu, He, Li, Bo, Tian. 2010-12-15. Integrability study on a generalized (2+1)-dimensional variable-coefficient Gardner model with symbolic computation. https://doi.org/10.1063/1.3494154

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