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Soliton Solution and Conservation Law of Gear-Grimshaw Model for Shallow Water Waves

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Triki H., Kara A., Bhrawy A., Biswas A.
Acta Physica Polonica A
|
2014
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vol. 125
|
issue 5
1099-1107
EN
This paper is going to obtain the soliton solution of the Gear-Grimshaw model that describes the dynamics of two-layered shallow water waves in oceans and rivers. The topological 1-soliton solution will be obtained by the ansatz method. There are several constraint conditions that will be taken care of. This will be followed by the model with power law nonlinearity. Subsequently, the conservation laws for this model will be derived by the aid of multiplier approach from the Lie symmetry analysis. Finally, the F-expansion method will extract a few more interesting solutions to the model.
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Application of Tanh Method to Complex Coupled Nonlinear Evolution Equations

100%
Abdelkawy M., Bhrawy A., Zerrad E., Biswas A.
Acta Physica Polonica A
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2016
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vol. 129
|
issue 3
278-283
EN
This paper studies the application of tanh method to address a few coupled nonlinear evolution equations that are in complex domain. There are soliton solutions as well as triangular solutions that are revealed with this integration scheme. The equations studied in this paper are applicable to various branches of applied and theoretical physics.
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