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

100%
Triki H., Kara A., Bhrawy A., Biswas A.
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vol. 125
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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.
2
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Exact Solutions and Conservation Laws of the Bogoyavlenskii Equation

100%
Inc M., Hashemi M., Isa Aliyu A.
Acta Physica Polonica A
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2018
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vol. 133
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issue 5
1133-1137
EN
In this paper, the Lie symmetry analysis method is performed for a Bogoyavlenskii equation. The symmetries and exact invariant solutions for the equation are retrieved for the first time. The conservation laws of the Bogoyavlenskii equation are constructed using the conservation laws theorem introduced by Ibragimov.
3
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Lie Symmetry Reductions, Exact Solutions and Conservation Laws of the Third Order Variant Boussinesq System

100%
Yaşar E., Giresunlu İ.
Acta Physica Polonica A
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2015
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vol. 128
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issue 3
252-255
EN
The Lie group method is applied to the third order variant Boussinesq system, which arises in the modelling of the water waves. The symmetry reductions and invariant solutions are obtained with respect to Lie point symmetry generators of the underlying system. In addition, we derive conservation laws of the variant Boussinesq system.
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