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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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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description 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.
doi_str_mv 10.1016/j.camwa.2018.12.010
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subjects Exponential functions
Interaction solution
Lump solution
Modified dispersive water wave equation
Quadratic equations
Quartic–linear form
Water waves
Wave dispersion
Wave equations
title Rational solutions and their interaction solutions of the (2+1)-dimensional modified dispersive water wave equation
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