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

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.

Solitary and Travelling Wave Solutions of Certain Nonlinear Diffusion-Reaction Equations

2020 ◽  
Author(s):  
Miftachul Hadi
Keyword(s):  
Nonlinear Diffusion ◽  
Travelling Wave ◽  
Diffusion Reaction ◽  
Travelling Wave Solutions ◽  
Wave Solutions ◽  
Reaction Equations

We review the work of Ranjit Kumar, R S Kaushal, Awadhesh Prasad. The work is still in progress.

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