In this paper we study nonlocal functionals whose kernels are homogeneous generalized functions. We also use such functionals to solve the Kortewegde Vries (KdV), the nonlinear Schrödinger (NLS) and the Davey-Stewartson (DS) equations. The solution of certain integrable equations in terms of formal power series was obtained in [4], [5]. In these papers the solution was expressed in a formal pow...

In this work G'/G-expansion method has been employed to solve (2+1)-dimensional dispersive long wave equation. It is shown that G'/G-expansion method, with the help of symbolic computation, provides a very effective and powerful mathematical tool, for solving this equation.

In this paper, the Exp-function method, with the aid of a symbolic computation system such as Maple, is applied to the (2+1) -dimensional Calogero Bogoyavlanskii Schiff equation. Exact and explicit generalized solitary solutions are obtained in more general forms. The free parameters can be determined by initial or boundary conditions. The method is straightforward and concise, and its applicat...

The (2+1)-dimensional “universal” variable separation formula (Tang, Lou and Zhang, Physical Review E 66, 046601 (2002)) is extended to a more general form for some (2+1)-dimensional integrable systems. Various independent arbitrary functions have been included in the extended formula. Starting from the universal formula and its extended form, a new type of solitons, foldons, is studied both an...

In this letter, we established a traveling wave solution by using cosine function algorithm for Gardnerequation and (2+1)-dimensional breaking soliton system. The cosine method is used to obtain theexact solution.