We apply the method of operator splitting on the generalized Korteweg{de Vries (KdV) equation ut +f(u)x+"uxxx = 0, by solving the nonlinear conservation law ut +f(u)x = 0 and the linear dispersive equation ut + "uxxx = 0 sequentially. We prove that if the approximation obtained by operator splitting converges, then the limit function is a weak solution of the generalized KdV equation. Convergen...

In this present work, the Kudryashov method and the functional variable method are used to construct exact solutions of the complex KdV equation. The Kudryashov method and the functional variable method are powerful methods for obtaining exact solutions of nonlinear evolution equations.

In this paper we use the modified tanh-coth method to solve the Kawahara and the modified Kawahara equations. New multiple traveling wave solutions are obtained for the Kawahara and the modified Kawahara equations. 2000 Mathematics Subject Classification: 35K01; 35J05.

By using solutions of an ordinary differential equation, an auxiliary equationmethod is described to seek exact solutions of variablecoefficient KdV-MKdV equation. As a result, more new exact nontravelling solutions, which include soliton solutions, combined soliton solutions, triangular periodic solutions, Jacobi elliptic function solutions, and combined Jacobi elliptic function solutions, for...