Bifurcation of travelling wave solutions for the modified dispersive water wave equation

2008 ◽  
Vol 69 (1) ◽  
pp. 151-166 ◽  
Author(s):  
Qian Liu ◽  
Yuqian Zhou ◽  
Weinian Zhang
Keyword(s):  
Wave Equation ◽  
Water Wave ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
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

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.

scholarly journals Elliptic Travelling Wave Solutions to a Generalized Boussinesq Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Abdelfattah El Achab
Keyword(s):  
Wave Equation ◽  
Elliptic Function ◽  
Function Method ◽  
Boussinesq Equation ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Weierstrass Elliptic Function ◽  
Wave Solutions ◽  
Generalized Boussinesq Equation

Travelling wave solutions for the generalized Boussinesq wave equation are studied by using the Weierstrass elliptic function method. As a result, some previously known solutions are recovered, and at the same time some new ones are also given, as well as integrable ones.

scholarly journals Travelling wave solutions for a surface wave equation in fluid mechanics

2016 ◽  
Vol 20 (3) ◽  
pp. 893-898 ◽  
Author(s):  
Yi Tian ◽  
Zai-Zai Yan
Keyword(s):  
Wave Equation ◽  
Fluid Mechanics ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Expansion Method ◽  
Travelling Wave ◽  
Linear Wave ◽  
Travelling Wave Solutions ◽  
Linear Wave Equation ◽  
Wave Solutions

This paper considers a non-linear wave equation arising in fluid mechanics. The exact traveling wave solutions of this equation are given by using G'/G-expansion method. This process can be reduced to solve a system of determining equations, which is large and difficult. To reduce this process, we used Wu elimination method. Example shows that this method is effective.

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
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