scholarly journals Validation of ANUGA hydraulic model using exact solutions to shallow water wave problems

2013 ◽  
Vol 423 ◽  
pp. 012029 ◽  
Author(s):  
S Mungkasi ◽  
S G Roberts
Keyword(s):  
Exact Solutions ◽  
Shallow Water ◽  
Water Wave ◽  
Hydraulic Model ◽  
Shallow Water Wave ◽  
Wave Problems

Exact solutions of a (2+1)-dimensional extended shallow water wave equation

2019 ◽  
Vol 28 (10) ◽  
pp. 100202 ◽  
Author(s):  
Feng Yuan ◽  
Jing-Song He ◽  
Yi Cheng
Keyword(s):  
Wave Equation ◽  
Exact Solutions ◽  
Shallow Water ◽  
Water Wave ◽  
Shallow Water Wave

scholarly journals Novel Exact Solutions of the Extended Shallow Water Wave and the Fokas Equations

2018 ◽  
Vol 22 ◽  
pp. 01022
Author(s):  
Serbay DURAN ◽  
Berat KARAAGAC ◽  
Alaattin ESEN
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Exact Solutions ◽  
Shallow Water ◽  
Water Wave ◽  
Expansion Method ◽  
Travelling Wave ◽  
Wave Transformation ◽  
Partial Differential ◽  
Shallow Water Wave

In this study, a Sine-Gordon expansion method for obtaining novel exact solutions of extended shallow water wave equation and Fokas equation is presented. All of the equations which are under consideration consist of three or four variable. In this method, first of all, partial differential equations are reduced to ordinary differential equations by the help of variable change called as travelling wave transformation, then Sine Gordon expansion method allows us to obtain new exact solutions defined as in terms of hyperbolic trig functions of considered equations. The newly obtained results showed that the method is successful and applicable and can be extended to a wide class of nonlinear partial differential equations.

scholarly journals New exact solutions of a generalized shallow water wave equation

2010 ◽  
Vol 82 (2) ◽  
pp. 025003 ◽  
Author(s):  
Bijan Bagchi ◽  
Supratim Das ◽  
Asish Ganguly
Keyword(s):  
Wave Equation ◽  
Exact Solutions ◽  
Shallow Water ◽  
Water Wave ◽  
Shallow Water Wave ◽  
New Exact Solutions

New Exact Solutions of (2+1)-Dimensional Generalization of Shallow Water Wave Equation by (G′/G)-Expansion Method

2010 ◽  
Vol 20-23 ◽  
pp. 1516-1521 ◽  
Author(s):  
Bang Qing Li ◽  
Mei Ping Xu ◽  
Yu Lan Ma
Keyword(s):  
Wave Equation ◽  
Exact Solutions ◽  
Shallow Water ◽  
Water Wave ◽  
Evolution Equations ◽  
Expansion Method ◽  
Nonlinear Evolution Equations ◽  
Hyperbolic Function ◽  
Function Solution ◽  
Shallow Water Wave

Extending a symbolic computation algorithm, namely, (G′/G)-expansion method, a new series of exact solutions are constructed for (2+1)-dimensional generalization of shallow water wave equation. These solutions included hyperbolic function solution, trigonometric function solution and rational function solution. The procedure can illustrate that the new algorithm is concise, powerful and straightforward, and it can also be applied to find exact solutions for other high dimensional nonlinear evolution equations.

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