A numerical study of [formula omitted]-periodic wave solutions to four integrable equations

Abstract

Based on the direct method proposed by A. Nakamura, we present a numerical process to derive N-periodic wave solutions of integrable equations. In particular, we investigate numerical 3-periodic wave solutions of the shallow water wave equation, modified generalized Vakhnenko equation, (2+1)-dimensional BKP equation and a (2+1)-dimensional Boussinesq equation. Numerical experiments are conducted using Gauss–Newton and Levenberg–Marquardt method, respectively. The comparison of the two numerical approaches is given.