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We present the projective Riccati equations method to obtainexact solutions for the generalized shallow water wave equation GSWW. We show the behavior of solutions with a graph.

Tipo de documento: Artículo - Article

Palabras clave: Nonlinear differential equation, travelling wave solution, Mathematica, projective Riccati equation method.





Source: http://www.bdigital.unal.edu.co


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Boletı́n de Matemáticas Nueva Serie, Volumen XIII No.
1 (2006), pp.
50–56 EXACT SOLUTIONS FOR THE GENERALIZED SHALLOW WATER WAVE EQUATION BY THE GENERAL PROJECTIVE RICCATI EQUATIONS METHOD CÉSAR A.
GÓMEZ (∗) ÁLVARO SALAS (∗∗) Abstract.
We present the projective Riccati equations method to obtain exact solutions for the generalized shallow water wave equation (GSWW). We show the behavior of solutions with a graph. Key words and phrases. Nonlinear differential equation, travelling wave solution, Mathematica, projective Riccati equation method. Resumen.
Presentamos el método proyectivo de ecuaciones de Riccati para obtener soluciones exactas de la ecuación generalizada de onda de agua poco profunda (GSWW).
Mostramos el comportamiento de las soluciones con una gráfica. Palabras claves.
Ecuación diferencial no lineal, solución de onda viajera, Mathematica, método proyectivo de ecuaciones de Riccati. Introduction The search of exact solutions of partial differential equations is of great importance, because these equations appear in complex physics phenomena, mechanics, chemistry, biology and engineering.
A variety of powerful and direct methods have been developed in this direction.
Among these are the inverse scattering method, Hirota´s method, Bäcklund transformations, tanh-function method, extended tanh-function method.
In the literature, Conte et al.[1] (∗) César A.
Gómez.
Department of Mathematics, Universidad Nacional de Colombia, Bogotá.
E-mail: cagomezsi@unal.edu.co (∗∗) Álvaro Salas.
Department of Mathematics, Universidad de Caldas, Manizales, Colombia.
E-mail : asalash2002@yahoo.com Web site: http:--www.alvarosalas.com . 50 EXACT SOLUTIONS FOR THE GENERALIZED SHALLOW WATER WAVE. 51 presented a general ansatz to seek more new solitary wave solutions of some NLPDE´s.
More recently, Yan [4] developed Conte´s method and presented the general projective Riccati equations method .
In this paper, we will use ...






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