Abundant Lump-Type Solutions and Interaction Solutions for a Nonlinear (3+1) Dimensional Model

Abundant Lump-Type Solutions and Interaction Solutions for a Nonlinear (3+1) Dimensional Model

We explore dynamical features of lump solutions as diversion and propagation in the space. Through the Hirota bilinear method and the Cole-Hopf transformation, lump-type solutions and their interaction solutions with one- or two-stripe solutions have been generated for a generalized (3+1) shallow wa...

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Main Authors: R. Sadat, M. Kassem, Wen-Xiu Ma
Format: Article
Language:English
Published: Hindawi Limited 2018-01-01
Series:Advances in Mathematical Physics
Online Access:http://dx.doi.org/10.1155/2018/9178480
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spelling doaj-4349d43a77284fb1916f7d596a01f9492021-07-02T01:29:18ZengHindawi LimitedAdvances in Mathematical Physics1687-91201687-91392018-01-01201810.1155/2018/91784809178480Abundant Lump-Type Solutions and Interaction Solutions for a Nonlinear (3+1) Dimensional ModelR. Sadat0M. Kassem1Wen-Xiu Ma2Department of Mathematics and Physics, Faculty of Engineering, Zagazig University, EgyptDepartment of Mathematics and Physics, Faculty of Engineering, Zagazig University, EgyptDepartment of Mathematics and Statistics, University of South Florida, Tampa, FL 33620, USAWe explore dynamical features of lump solutions as diversion and propagation in the space. Through the Hirota bilinear method and the Cole-Hopf transformation, lump-type solutions and their interaction solutions with one- or two-stripe solutions have been generated for a generalized (3+1) shallow water-like (SWL) equation, via symbolic computations associated with three different ansatzes. The analyticity and localization of the resulting solutions in the (x,y,z, and t) space have been analyzed. Three-dimensional plots and contour plots are made for some special cases of the solutions to illustrate physical motions and peak dynamics of lump soliton waves in higher dimensions. The study of lump-type solutions moderates the visuality of optics media and oceanography waves.http://dx.doi.org/10.1155/2018/9178480
collection DOAJ
language English
format Article
sources DOAJ
author R. Sadat
M. Kassem
Wen-Xiu Ma
spellingShingle R. Sadat
M. Kassem
Wen-Xiu Ma
Abundant Lump-Type Solutions and Interaction Solutions for a Nonlinear (3+1) Dimensional Model
Advances in Mathematical Physics
author_facet R. Sadat
M. Kassem
Wen-Xiu Ma
author_sort R. Sadat
title Abundant Lump-Type Solutions and Interaction Solutions for a Nonlinear (3+1) Dimensional Model
title_short Abundant Lump-Type Solutions and Interaction Solutions for a Nonlinear (3+1) Dimensional Model
title_full Abundant Lump-Type Solutions and Interaction Solutions for a Nonlinear (3+1) Dimensional Model
title_fullStr Abundant Lump-Type Solutions and Interaction Solutions for a Nonlinear (3+1) Dimensional Model
title_full_unstemmed Abundant Lump-Type Solutions and Interaction Solutions for a Nonlinear (3+1) Dimensional Model
title_sort abundant lump-type solutions and interaction solutions for a nonlinear (3+1) dimensional model
publisher Hindawi Limited
series Advances in Mathematical Physics
issn 1687-9120
1687-9139
publishDate 2018-01-01
description We explore dynamical features of lump solutions as diversion and propagation in the space. Through the Hirota bilinear method and the Cole-Hopf transformation, lump-type solutions and their interaction solutions with one- or two-stripe solutions have been generated for a generalized (3+1) shallow water-like (SWL) equation, via symbolic computations associated with three different ansatzes. The analyticity and localization of the resulting solutions in the (x,y,z, and t) space have been analyzed. Three-dimensional plots and contour plots are made for some special cases of the solutions to illustrate physical motions and peak dynamics of lump soliton waves in higher dimensions. The study of lump-type solutions moderates the visuality of optics media and oceanography waves.
url http://dx.doi.org/10.1155/2018/9178480
work_keys_str_mv AT rsadat abundantlumptypesolutionsandinteractionsolutionsforanonlinear31dimensionalmodel
AT mkassem abundantlumptypesolutionsandinteractionsolutionsforanonlinear31dimensionalmodel
AT wenxiuma abundantlumptypesolutionsandinteractionsolutionsforanonlinear31dimensionalmodel
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