Abundant Lump-Type Solutions and Interaction Solutions for a Nonlinear (3+1) Dimensional Model-Reference-Cited by-同舟云学术

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

Published:2018-12-10 Issue: Volume:2018 Page:1-8
ISSN:1687-9120
Container-title:Advances in Mathematical Physics
language:en
Short-container-title:Advances in Mathematical Physics

Author:

Sadat R.¹^ORCID,Kassem M.¹,Ma Wen-Xiu²³⁴⁵^ORCID

Affiliation:

1. Department of Mathematics and Physics, Faculty of Engineering, Zagazig University, Egypt

2. Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620, USA

3. Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia

4. College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, Shandong, China

5. International Institute for Symmetry Analysis and Mathematical Modelling, Department of Mathematical Sciences, North-West University, Mafikeng Campus, Mmabatho 2735, South Africa

Abstract

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.

Publisher

Hindawi Limited

Subject

Applied Mathematics,General Physics and Astronomy

Link

http://downloads.hindawi.com/journals/amp/2018/9178480.pdf

Reference27 articles.

1. Explicit Solutions for the (2 + 1)-Dimensional Jaulent–Miodek Equation Using the Integrating Factors Method in an Unbounded Domain

2. Shifts of annihilation radiation energy from the electron rest mass energy for positons annihilating in copper and sodium

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