On the new wave solutions to the MCH equation

被引：51
作者：
Abdelrahman, M. A. E. [1 ,2 ]
Sohaly, M. A. [2 ]
机构：
[1] Taibah Univ, Dept Math, Coll Sci, Al Madinah Al Munawarah, Saudi Arabia
[2] Mansoura Univ, Fac Sci, Dept Math, Mansoura 35516, Egypt
来源：
INDIAN JOURNAL OF PHYSICS | 2019年 / 93卷 / 07期
关键词：
exp(-phi(xi))-expansion technique; Sine-cosine technique; Deterministic (random) MCH equation; Deterministic (stochastic) solitary wave solutions; Convergence; NONLINEAR EVOLUTION-EQUATIONS; ELLIPTIC FUNCTION-METHOD; F-EXPANSION METHOD; SINE-COSINE METHOD; TANH METHOD; (G'/G)-EXPANSION METHOD; SOLITONS; COMPACT;
D O I：
10.1007/s12648-018-1354-6
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
We will apply two mathematical methods, namely the exp(-phi())-expansion and sine-cosine in deterministic and stochastic ways for solving the deterministic and stochastic cases of the simplified MCH equation. This nonlinear equation can be turned into another nonlinear ordinary differential equation by appropriate transformation. The methods that we use are efficient and powerful in solving wide classes of nonlinear equations. The solutions obtained are in the form of trigonometric, hyperbolic, exponential and rational functions and a variety of special solutions like kink-shaped, bell-type soliton solutions. Moreover, these solutions reflect some interesting physical interpretation for nonlinear problems. We will also study the stochastic case from the point random wave transformation or some disturbances in the equation itself. The convergence conditions will be discussed.
引用
收藏
页码：903 / 911
页数：9
相关论文
共 49 条
[1]   A note on Riccati-Bernoulli Sub-ODE method combined with complex transform method applied to fractional differential equations [J].
Abdelrahman, Mahmoud A.E. .
Nonlinear Engineering, 2018, 7 (04) :279-285
[2]  
Abdelrahman M. A. E., 2017, J. Phys. Math., V8, DOI [10.4172/2090-0902.1000214, DOI 10.1016/10.4172/2090-0902.1000214]
[3]  
Abdelrahman M A E, 2014, INT J NONLINEAR SCI, DOI [10.1515/ijnsns-0121, DOI 10.1515/IJNSNS-0121]
[4]   On the Shallow Water Equations [J].
Abdelrahman, Mahmoud A. E. .
ZEITSCHRIFT FUR NATURFORSCHUNG SECTION A-A JOURNAL OF PHYSICAL SCIENCES, 2017, 72 (09) :873-879
[5]   Solitary waves for the nonlinear Schrodinger problem with the probability distribution function in the stochastic input case [J].
Abdelrahman, Mahmoud A. E. ;
Sohaly, M. A. .
EUROPEAN PHYSICAL JOURNAL PLUS, 2017, 132 (08)
[6]   Global solutions for the ultra-relativistic Euler equations [J].
Abdelrahman, Mahmoud A. E. .
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2017, 155 :140-162
[7]   The ultra-relativistic Euler equations [J].
Abdelrahman, Mahmoud A. E. ;
Kunik, Matthias .
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2015, 38 (07) :1247-1264
[8]  
Alam MN., 2015, J. Assoc. Arab Univ. Basic Appl. Sci, V17, P6
[9]  
AMINIKHAD H, 2009, NUMER METH PART D E, V26, P1427
[10]   An efficient Jacobi pseudospectral approximation for nonlinear complex generalized Zakharov system [J].
Bhrawy, A. H. .
APPLIED MATHEMATICS AND COMPUTATION, 2014, 247 :30-46
12345