Numerical generation of periodic traveling wave solutions of some nonlinear dispersive wave systems

In this paper a numerical procedure to generate approximations to periodic traveling wave profiles of some nonlinear dispersive wave systems is introduced. The method is based on a suitable modification of a fixed point algorithm of Petviashvili type and solves several drawbacks of some previous algorithms presented in the literature. By way of illustration, the method is applied to generate numerically periodic traveling waves of two problems of interest: the fractional KdV type equations and the extended Boussinesq system. We propose a method to compute periodic traveling waves.The method can be applied to some nonlinear dispersive systems.It is checked in fractional KdV equations and Boussinesq systems.