Complexiton and resonant multiple wave solutions to the (2+1)-dimensional Konopelchenko–Dubrovsky equation

Abstract

In this paper, the (2+1)-dimensional Konopelchenko–Dubrovsky (KD) equation is investigated. Using the Hirota direct method and linear superposition principle, the complexiton and resonant multiple wave solutions are successfully constructed. For the Hirota direct method, it is essential that finding the bilinear form to the KD equation and applying its 2N-soliton formulation in real field to build the N-complexiton solutions under the action of pairs of conjugate wave variables. The linear superposition in real field of exponential traveling waves can generate the resonant multiple wave solutions, and then generalize linear superposition principle to complex field, we obtain some new resonant multiple wave type solutions. The phenomena of complexiton, resonant multiple wave and new resonant multiple wave type solutions are presented by figures.