Regarding some novel exponential travelling wave solutions to the Wu–Zhang system arising in nonlinear water wave model

2018 ◽  
Vol 93 (8) ◽  
pp. 1031-1039 ◽  
Author(s):  
G. Yel ◽  
H. M. Baskonus ◽  
H. Bulut
Keyword(s):  
Water Wave ◽  
Wave Model ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Wave Solutions

scholarly journals Dynamical behaviour of travelling wave solutions to the conformable time-fractional modified Liouville and mRLW equations in water wave mechanics

Heliyon ◽  
2021 ◽  
Vol 7 (8) ◽  
pp. e07704
Author(s):  
Abdulla - Al Mamun ◽  
Samsun Nahar Ananna ◽  
Tianqing An ◽  
Nur Hasan Mahmud Shahen ◽  
Md. Asaduzzaman ◽  
...  
Keyword(s):  
Water Wave ◽  
Travelling Wave ◽  
Dynamical Behaviour ◽  
Travelling Wave Solutions ◽  
Wave Mechanics ◽  
Wave Solutions

Exact travelling wave solutions for the generalized shallow water wave equation

2003 ◽  
Vol 17 (1) ◽  
pp. 121-126 ◽  
Author(s):  
S.A. Elwakil ◽  
S.K. El-labany ◽  
M.A. Zahran ◽  
R. Sabry
Keyword(s):  
Wave Equation ◽  
Shallow Water ◽  
Water Wave ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Shallow Water Wave ◽  
Wave Solutions

scholarly journals Exact Solutions of Travelling Wave Model via Dynamical System Method

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Heng Wang ◽  
Longwei Chen ◽  
Hongjiang Liu
Keyword(s):  
Dynamical System ◽  
Solitary Wave ◽  
Elliptic Functions ◽  
Wave Model ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Solitary Wave Solutions ◽  
Jacobian Elliptic Functions ◽  
Wave Solutions ◽  
Periodic Travelling Wave

By using the method of dynamical system, the exact travelling wave solutions of the coupled nonlinear Schrödinger-Boussinesq equations are studied. Based on this method, the bounded exact travelling wave solutions are obtained which contain solitary wave solutions and periodic travelling wave solutions. The solitary wave solutions and periodic travelling wave solutions are expressed by the hyperbolic functions and the Jacobian elliptic functions, respectively. The results show that the presented findings improve the related previous conclusions. Furthermore, the numerical simulations of the solitary wave solutions and the periodic travelling wave solutions are given to show the correctness of our results.

New travelling wave solutions for coupled fractional variant Boussinesq equation and approximate long water wave equation

2015 ◽  
Vol 25 (1) ◽  
pp. 33-40 ◽  
Author(s):  
Limei Yan
Keyword(s):  
Wave Equation ◽  
Water Wave ◽  
Boussinesq Equation ◽  
Travelling Wave ◽  
Hyperbolic Function ◽  
Travelling Wave Solutions ◽  
Rational Solutions ◽  
Content Type ◽  
Wave Solutions ◽  
Hyperbolic Function Solutions

Purpose – The purpose of this paper is to apply the fractional sub-equation method to research on coupled fractional variant Boussinesq equation and fractional approximate long water wave equation. Design/methodology/approach – The algorithm is implemented with the aid of fractional Ricatti equation and the symbol computational system Mathematica. Findings – New travelling wave solutions, which include generalized hyperbolic function solutions, generalized trigonometric function solutions and rational solutions, for these two equations are obtained. Originality/value – The algorithm is demonstrated to be direct and precise, and can be used for many other nonlinear fractional partial differential equations. The fractional derivatives described in this paper are in the Jumarie's modified Riemann-Liouville sense.

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