Lump solutions and interaction phenomena of the (3 + 1)-dimensional nonlinear evolution equations

Lump solutions and interaction phenomena of the (3 + 1)-dimensional nonlinear evolution... PurposeThe purpose of this study is to examine the lump solutions of the (3 + 1)-dimensional nonlinear evolution equations by considering a (3 + 1)-dimensional generalized Kadomtsev–Petviashvili (gKP) equation and a (3 + 1)-dimensional variable-coefficient generalized B-type Kadomtsev–Petviashvili (vcgBKP) equation as examples.Design/methodology/approachBased on Hirota’s bilinear theory, a direct method is used to examine the lump solutions of these two equations.FindingsThe complete non-elastic interaction solutions between a lump and a stripe are also discussed for the equations, which show that the lump solitons are swallowed by the stripe solitons.Originality/valueThe dynamics of these solutions are analyzed to enrich the diversity of the dynamics of high-dimensional KP-type nonlinear wave equations. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png International Journal of Numerical Methods for Heat & Fluid Flow Emerald Publishing

Lump solutions and interaction phenomena of the (3 + 1)-dimensional nonlinear evolution equations

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Publisher
Emerald Publishing
Copyright
Copyright © Emerald Group Publishing Limited
ISSN
0961-5539
DOI
10.1108/HFF-02-2019-0160
Publisher site
See Article on Publisher Site

Abstract

PurposeThe purpose of this study is to examine the lump solutions of the (3 + 1)-dimensional nonlinear evolution equations by considering a (3 + 1)-dimensional generalized Kadomtsev–Petviashvili (gKP) equation and a (3 + 1)-dimensional variable-coefficient generalized B-type Kadomtsev–Petviashvili (vcgBKP) equation as examples.Design/methodology/approachBased on Hirota’s bilinear theory, a direct method is used to examine the lump solutions of these two equations.FindingsThe complete non-elastic interaction solutions between a lump and a stripe are also discussed for the equations, which show that the lump solitons are swallowed by the stripe solitons.Originality/valueThe dynamics of these solutions are analyzed to enrich the diversity of the dynamics of high-dimensional KP-type nonlinear wave equations.

Journal

International Journal of Numerical Methods for Heat & Fluid FlowEmerald Publishing

Published: Sep 2, 2019

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