The new exact solutions for the deterministic and stochastic (2+1)-dimensional equations in natural sciences

被引：21

作者：

Abdelrahman, Mahmoud A. E. ^{[1
,2
]}

Sohaly, M. A. ^{[2
]}

Alharbi, Abdulghani ^{[1
]}

机构：

[1] Taibah Univ, Coll Sci, Dept Math, Al Madinah Al Munawarah, Saudi Arabia

[2] Mansoura Univ, Fac Sci, Dept Math, Mansoura 35516, Egypt

来源：

JOURNAL OF TAIBAH UNIVERSITY FOR SCIENCE | 2019年 / 13卷 / 01期

关键词：

Riccati-Bernoulli sub-ODE method; nonlinear (stochastic) partial differential equations; cKG equation; ZK-MEW equation; Backlund transformation; travelling wave solutions; SOLITARY WAVE SOLUTIONS; ELLIPTIC FUNCTION-METHOD; EXP-FUNCTION METHOD; F-EXPANSION METHOD; TANH METHOD; (G'/G)-EXPANSION METHOD; NONLINEAR EVOLUTION; OPTICAL SOLITONS; BURGERS-EQUATION; GORDON EQUATION;

D O I：

10.1080/16583655.2019.1644832

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

This paper poses the Riccati-Bernoulli sub-ODE method in order to find the exact (random) travelling wave solutions for the (2+1)-dimensional cubic nonlinear Klein-Gordon (cKG) equation and the (2+1)-dimensional nonlinear Zakharov-Kuznetsov modified equal width (ZK-MEW) equation. The obtained travelling wave solutions are expressed by the hyperbolic, trigonometric and rational functions. Indeed, these solutions reflect some interesting physical interpretation for nonlinear phenomena. We discuss our method in deterministic case and in a random case. Additionally, we can show and discuss this method under some random distributions. Finally, some three-dimensional graphics of some solutions have been illustrated.

引用

页码：834 / 843

页数：10

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