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Application of the method of simplest equation for obtaining exact traveling-wave solutions for two classes of model PDEs from ecology and population dynamics

✍ Scribed by Nikolay K. Vitanov; Zlatinka I. Dimitrova

Publisher: Elsevier Science
Year: 2010
Tongue: English
Weight: 252 KB
Volume: 15
Category: Article
ISSN: 1007-5704
DOI: 10.1016/j.cnsns.2009.11.029

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✦ Synopsis

of simplest equation Exact traveling-wave solutions a b s t r a c t We search for traveling-wave solutions of two classes of equations: (I.) Class of reaction-diffusion equations

Above a, b, c are parameters and D and F depend on the population density Q. We obtain such solutions by the modified method of simplest equation for the cases when the simplest equation is the equation of Bernoulli or the equation of Riccati. On the basis of the appropriate ansatz the PDEs are reduced to nonlinear algebraic systems of relationships among the parameters of the equations and the parameters of the solution. By means of these systems we obtain numerous solutions for PDEs belonging to the investigated classes of equations.

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