Breather, multi-shock waves and localized excitation structure solutions to the Extended BKP–Boussinesq equation

Abstract

The extended BKP–Boussinesq equation is considered to construct abundant breather waves, multi-shocks waves and localized excitation solutions. We first transform the original model to its bilinear form through a logarithmic transformation relation. Then, by setting a simple ansatz as a combinations of exponential and sinusoidal functions to obtain various breather waves solutions. We successfully archive five types of breather waves and depict graphically. Taking Burger model as an auxiliary equation, we derive multi-shock waves solutions to illustrate the overtaking collisions and energy distribution of the extended model sufficiently. Finally, we keep a simple variable separable ansatz solution to derive localized excitation structures of the model. Most of these solutions are found for the first time. Furthermore, the results disclose that the new approaches are very direct, elementary, effective and can be used for many other NLPDEs, which develop the various types of dynamical properties of any wave model.