The numerical solution of Boussinesq equation for shallow water waves

2020 ◽  
Author(s):  
Prashant Patel ◽  
Prashant Kumar ◽  
Rajni
Keyword(s):  
Numerical Solution ◽  
Shallow Water ◽  
Water Waves ◽  
Boussinesq Equation ◽  
Shallow Water Waves

scholarly journals Gaussian solitary waves to Boussinesq equation with dual dispersion and logarithmic nonlinearity

2018 ◽  
Vol 23 (6) ◽  
pp. 942-950 ◽  
Author(s):  
Anjan Biswasa ◽  
Mehmet Ekici ◽  
Abdullah Sonmezoglu
Keyword(s):  
Solitary Wave ◽  
Shallow Water ◽  
Solitary Waves ◽  
Water Waves ◽  
Trial Function ◽  
Boussinesq Equation ◽  
Solitary Wave Solutions ◽  
Shallow Water Waves ◽  
Wave Solutions ◽  
Extended Trial

This paper discusses shallow water waves that is modeled with Boussinesq equation that comes with dual dispersion and logarithmic nonlinearity. The extended trial function scheme retrieves exact Gaussian solitary wave solutions to the model.

scholarly journals Nonlinear self adjointness, conservation laws and exact solutions of ill-posed Boussinesq equation

Open Physics ◽  
2016 ◽  
Vol 14 (1) ◽  
pp. 37-43 ◽  
Author(s):  
Emrullah Yaşar ◽  
Sait San ◽  
Yeşim Sağlam Özkan
Keyword(s):  
Conservation Laws ◽  
Exact Solutions ◽  
Shallow Water ◽  
Water Waves ◽  
Function Method ◽  
Boussinesq Equation ◽  
Lie Point Symmetries ◽  
Shallow Water Waves ◽  
Non Linear ◽  
Ill Posed

AbstractIn this work, we consider the ill-posed Boussinesq equation which arises in shallow water waves and non-linear lattices. We prove that the ill-posed Boussinesq equation is nonlinearly self-adjoint. Using this property and Lie point symmetries, we construct conservation laws for the underlying equation. In addition, the generalized solitonary, periodic and compact-like solutions are constructed by the exp-function method.

scholarly journals Dynamics of shallow water waves with Boussinesq equation

2013 ◽  
Author(s):  
A.J.M. Jawad ◽  
M.D. Petković ◽  
P. Laketa ◽  
A. Biswas
Keyword(s):  
Shallow Water ◽  
Water Waves ◽  
Boussinesq Equation ◽  
Shallow Water Waves

scholarly journals Coupling Conditions for Water Waves at Forks

Symmetry ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 434 ◽  
Author(s):  
Jean-Guy Caputo ◽  
Denys Dutykh ◽  
Bernard Gleyse
Keyword(s):  
Conservation Laws ◽  
Numerical Solution ◽  
Shallow Water ◽  
Water Waves ◽  
Large Amplitude ◽  
Narrow Channel ◽  
Effective Model ◽  
Interface Conditions ◽  
Shallow Water Waves ◽  
Coupling Conditions

We considered the propagation of nonlinear shallow water waves in a narrow channel presenting a fork. We aimed at computing the coupling conditions for a 1D effective model, using 2D simulations and an analysis based on the conservation laws. For small amplitudes, this analysis justifies the well-known Stoker interface conditions, so that the coupling does not depend on the angle of the fork. We also find this in the numerical solution. Large amplitude solutions in a symmetric fork also tend to follow Stoker’s relations, due to the symmetry constraint. For non symmetric forks, 2D effects dominate so that it is necessary to understand the flow inside the fork. However, even then, conservation laws give some insight in the dynamics.

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