Breathers, resonant multiple waves and complexiton solutions of a (2+1)-dimensional nonlinear evolution equation

Based on the Hirota bilinear form of a (2+1)-dimensional equation, breathers and resonant multiple waves as well as complexiton solutions are considered in this paper. First, the breather waves are constructed via employing the extend homoclinic test method. By calculation, two kinds of solutions are obtained. Through analysis, three pairs of breathers consisting of hyperbolic functions and trigonometric functions are derived. Furthermore, a rouge wave solution is deduced by applying the Taylor expansion method to a obtained breather wave. In addition, related figures are plotted to illustrate the dynamical features of these obtained solutions. Then, two types of the resonant multi-soliton solutions are obtained by applying the linear superposition principle to the the Hirota bilinear form. At the same time, 3D profiles and 2D density plots are presented to depict the intersection progression of wave motion. Finally, the complexiton solutions are constructed according to the yielded resonant multi-soliton solutions by further utilizing the linear superposition principle. By considering different domain fields, several types of complexiton solutions including the positive ones are derived. Moreover, related 3D and 2D figures are plotted for the obtained results in order to vividly exhibit their dynamics properties.