A generalized ansatz method (SEsM) is shown to reproduce Hirota's KdV multisoliton solutions and to yield an exact solution of a nonintegrable fifth-order KdV-type equation.
Discussion on exp-function method and modified method of simplest equation
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abstract
We discuss the relation between the modified method of simplest equation and the exp-function method. First on the basis of our experience from the application of the method of simplest equation we generalize the exp-function ansatz. Then we apply the ansatz for obtaining exact solutions for members of a class of nonlinear PDEs which contains as particular cases several nonlinear PDEs that model the propagation of water waves.
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The Simple Equations Method (SEsM) and the use of exponential functions for obtaining simple and multisoliton solutions of some nonlinear partial differential equations
A generalized ansatz method (SEsM) is shown to reproduce Hirota's KdV multisoliton solutions and to yield an exact solution of a nonintegrable fifth-order KdV-type equation.