Rational solutions and their interaction solutions of the (2+1)-dimensional modified dispersive water wave equation

A bilinear form for the modified dispersive water wave (mDWW) equation is presented by the truncated Painlevé series, which does not lead to lump solutions. In order to get lump solutions, a pair of quartic–linear forms for the mDWW equation is constructed by selecting a suitable seed solution of th...

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Bibliographic Details
Published in:Computers & mathematics with applications (1987) 2019-04, Vol.77 (8), p.2086-2095
Main Authors: Ren, Bo, Ma, Wen-Xiu, Yu, Jun
Format: Article
Language:English
Subjects:
Exponential functions
Interaction solution
Lump solution
Modified dispersive water wave equation
Quadratic equations
Quartic–linear form
Water waves
Wave dispersion
Wave equations
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Summary:A bilinear form for the modified dispersive water wave (mDWW) equation is presented by the truncated Painlevé series, which does not lead to lump solutions. In order to get lump solutions, a pair of quartic–linear forms for the mDWW equation is constructed by selecting a suitable seed solution of the mDWW equation in the truncated Painlevé series. Rational solutions are then computed by searching for positive quadratic function solutions. A regular nonsingular rational solution can describe a lump in this model. By combining quadratic functions with exponential functions, some novel interaction solutions are founded, including interaction solutions between a lump and a one-kink soliton, a bi-lump and a one-stripe soliton, and a bi-lump and a two-stripe soliton. Concrete lumps and their interaction solutions are illustrated by 3d-plots and contour plots.
ISSN:0898-1221
1873-7668
DOI:10.1016/j.camwa.2018.12.010