Studying on the Complex and Mixed Dark-Bright Travelling Wave Solutions of the Generalized KP-BBM Equation

2021 ◽  
pp. 17-38
Author(s):  
Haci Mehmet Baskonus ◽  
Ajay Kumar ◽  
M.S. Rawat ◽  
Bilgin Senel ◽  
Gulnur Yel ◽  
...  
Keyword(s):  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Wave Solutions ◽  
Bbm Equation

Bifurcations of travelling wave solutions for the generalized KP–BBM equation

2010 ◽  
Vol 216 (10) ◽  
pp. 2881-2890 ◽  
Author(s):  
Shengqiang Tang ◽  
Xiaoliang Huang ◽  
Wentao Huang
Keyword(s):  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Wave Solutions ◽  
Bbm Equation

scholarly journals Assessment of the Exact Solutions of the Space and Time Fractional Benjamin-Bona-Mahony Equation via the G′/G-Expansion Method, Modified Simple Equation Method, and Liu’s Theorem

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Olusola Kolebaje ◽  
Oyebola Popoola
Keyword(s):  
Expansion Method ◽  
Travelling Wave ◽  
Simple Equation ◽  
Equation Method ◽  
Travelling Wave Solutions ◽  
Space And Time ◽  
Wave Solutions ◽  
Liouville Derivative ◽  
Modified Simple Equation Method ◽  
Bbm Equation

Exact travelling wave solutions to the space and time fractional Benjamin-Bona-Mahony (BBM) equation defined in the sense of Jumarie’s modified Riemann-Liouville derivative via the (G′/G) expansion and the modified simple equation methods are presented in this paper. A fractional complex transformation was applied to turn the fractional BBM equation into an equivalent integer order ordinary differential equation. New complex type travelling wave solutions to the space and time fractional BBM equation were obtained with Liu’s theorem. The modified simple equation method is not effective for constructing solutions to the fractional BBM equation.

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.

scholarly journals Singularity analysis and analytic solutions for the Benney–Gjevik equations

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Andronikos Paliathanasis ◽  
Genly Leon ◽  
P. G. L. Leach
Keyword(s):  
Evolution Equations ◽  
Singularity Analysis ◽  
Analytic Solutions ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Painlevé Test ◽  
Wave Solutions ◽  
Algebraic Solutions

Abstract We apply the Painlevé test for the Benney and the Benney–Gjevik equations, which describe waves in falling liquids. We prove that these two nonlinear 1 + 1 evolution equations pass the singularity test for the travelling-wave solutions. The algebraic solutions in terms of Laurent expansions are presented.

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