Computational examples of soliton-like classes of solutions of some higher-order evolution equations

Article type: Research Article

Authors: Huber, Alfred

Affiliations: Prottesweg 2a, A-8062 Kumberg, Austria. E-mail: [email protected]

Abstract: A computational approach is used to find new solitary solutions of some nonlinear partial differential equations of higher order. The usual starting point is a special transformation converting the equation under consideration in its two variables x and t into a nonlinear ordinary differential equation in the single variable ξ. When we consider the method of hyperbolic functions, new distinctive classes of solutions of physical relevance result. The new feature of this paper is the fact that we are able to calculate distinctive classes of solitary solutions which cannot be found in the literature. In other words using this method the solution manifold is augmented by further classes of solution functions. Simultaneously we stress the necessity of such sophisticated methods since a general theory of nonlinear partial differential equations does not exist. Otherwise this paper is a natural completion of our recent results using alternative approaches for calculating soliton-like solutions.

Keywords: Nonlinear partial differential equations, solitary solutions, Hyperbolic Function Method

DOI: 10.3233/JCM-2011-0289

Journal: Journal of Computational Methods in Sciences and Engineering, vol. 11, no. 1-2, pp. 13-23, 2011