Based on a new first-order nonlinear ordinary differential equation with a sixth-degree nonlinear term and some of its special solutions, a generalized transformation method is proposed to obtain more general exact solutions of the (2+1)-dimensional Konopelchenko-Dubrovsky equations. As a result, new exact nontravelling wave solutions are obtained including soliton-like solutions and trigonomet...

On the basis of the computer symbolic system Maple and the extended hyperbolic function method, we develop a more mathematically rigorous and systematic procedure for constructing exact solitary wave solutions and exact periodic traveling wave solutions in triangle form of various nonlinear partial differential equations that are with physical backgrounds. Compared with the existing methods, th...

An extended ( ′ G )–expansion method is obtained by improving the form of solution in ( G′ G )– expansion method which is proposed in recent years. By using the extended ( ′ G )–expansion method and with the aid of homogeneous balance principle, many explicit and exact travelling wave solutions with two arbitrary parameters to the Klein-Gordon equation are presented, including the hyperbolic so...

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 first integral method is an efficient method for obtaining exact solutions of some nonlinear partial differential equations. this method can be applied to non integrable equations as well as to integrable ones. in this paper, the first integral method is used to construct exact solutions of the 2d ginzburg-landau equation.

A method is given to construct globally analytic (in space and time) exact solutions to the focusing cubic nonlinear Schrödinger equation on the line. An explicit formula and its equivalents are presented to express such exact solutions in a compact form in terms of matrix exponentials. Such exact solutions can alternatively be written explicitly as algebraic combinations of exponential, trigon...