Resonant multiple wave solutions, complexiton solutions and rogue waves of a generalized (3+1)-dimensional nonlinear wave in liquid with gas bubbles

Abstract

In this paper, the generalized (3+1)-dimensional nonlinear wave in liquid with gas bubbles is investigated. It describes the dynamics of nonlinear waves in hydrodynamics. On the one hand, we construct a class of special N-wave solutions by applying the linear superposition principle, resonant multiple wave solutions and complexiton solutions are derived. On the other hand, the rational breather wave and rogue wave solutions of the equation are also obtained by employing the extended homoclinic test method. Finally, all these solutions are presented via 3-dimensional plots and density plots with choices some special parameters to show the dynamic characteristics.