NEW TRAVELING WAVE SOLUTIONS OF THE (3+1)-DIMENSIONAL GENERALIZED BREAKING SOLITON EQUATION

In this paper, we will study solutions of the (3+1)-dimensional generalized breaking soliton (gBS) equation which used to describe the interaction phenomena between Riemann wave and long wave via three space variables in nonlinear media. Firstly, we transform (3+1)-dimensional gBS equation to the bilinear form. Secondly, we apply the three-wave method to study bilinear form and then get many kinds of solutions for (3+1)-dimensional gBS equation, concluding periodic solitary wave solutions, bell solitary wave solutions, two-soliton solutions, breather lump wave solutions, et al. These solutions can describe interaction between waves and are presented by 3D and 2D graphs. Finally, we analyze the resolving thoughts of extended homoclinic test method and its correlation of three-wave method. Our results show the significance and efficiency of these methods.