Exact Solutions of Generalized Riemann Problem for Nonhomogeneous Shallow Water Equations

2020 ◽  
Vol 51 (3) ◽  
pp. 1225-1237
Author(s):  
Sueet Millon Sahoo ◽  
T. Raja Sekhar ◽  
G. P. Raja Sekhar
Keyword(s):  
Exact Solutions ◽  
Shallow Water ◽  
Riemann Problem ◽  
Shallow Water Equations ◽  
Generalized Riemann Problem

scholarly journals Approximate Traveling Wave Solutions of Coupled Whitham-Broer-Kaup Shallow Water Equations by Homotopy Analysis Method

2008 ◽  
Vol 2008 ◽  
pp. 1-8 ◽  
Author(s):  
M. M. Rashidi ◽  
D. D. Ganji ◽  
S. Dinarvand
Keyword(s):  
Exact Solutions ◽  
Shallow Water ◽  
Homotopy Analysis Method ◽  
Shallow Water Equations ◽  
Traveling Wave ◽  
Nonlinear Partial Differential Equations ◽  
Traveling Wave Solutions ◽  
Analysis Method ◽  
Wave Solutions ◽  
Homotopy Analysis

The homotopy analysis method (HAM) is applied to obtain the approximate traveling wave solutions of the coupled Whitham-Broer-Kaup (WBK) equations in shallow water. Comparisons are made between the results of the proposed method and exact solutions. The results show that the homotopy analysis method is an attractive method in solving the systems of nonlinear partial differential equations.

scholarly journals Symmetries and exact solutions of the rotating shallow-water equations

2009 ◽  
Vol 20 (5) ◽  
pp. 461-477 ◽  
Author(s):  
A. A. CHESNOKOV
Keyword(s):  
Exact Solutions ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Water Model ◽  
New Class ◽  
New Exact Solutions ◽  
Time Periodic Solutions ◽  
Rotating Shallow Water ◽  
Rotating Shallow Water Equations ◽  
Time Periodic

Lie symmetry analysis is applied to study the non-linear rotating shallow-water equations. The 9-dimensional Lie algebra of point symmetries admitted by the model is found. It is shown that the rotating shallow-water equations can be transformed to the classical shallow-water model. The derived symmetries are used to generate new exact solutions of the rotating shallow-water equations. In particular, a new class of time-periodic solutions with quasi-closed particle trajectories is constructed and studied. The symmetry reduction method is also used to obtain some invariant solutions of the model. Examples of these solutions are presented with a brief physical interpretation.

Computational study of some nonlinear shallow water equations

Open Physics ◽  
2013 ◽  
Vol 11 (4) ◽  
Author(s):  
Ali Bhrawy ◽  
Mohamed Abdelkawy
Keyword(s):  
Exact Solutions ◽  
Shallow Water ◽  
Periodic Solutions ◽  
Shallow Water Equations ◽  
Computational Study ◽  
Expansion Method ◽  
Coastal Areas ◽  
Atmospheric Modeling ◽  
Hydraulic Engineering ◽  
Nonlinear Shallow Water Equations

AbstractThe shallow water equations have wide applications in ocean, atmospheric modeling and hydraulic engineering, also they can be used to model flows in rivers and coastal areas. In this article we obtained exact solutions of three equations of shallow water by using $\frac{{G'}} {G} $-expansion method. Hyperbolic and triangular periodic solutions can be obtained from the $\frac{{G'}} {G} $-expansion method.

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