A novel (2+1)-dimensional Sawada-Kotera type system: multisoliton solution and variable separation solution

Abstract

A novel (2+1)-dimensional Sawada-Kotera type system is considered. The existence of three-soliton and four-soliton solutions with constraints on wave numbers is confirmed. Other intriguing solutions, such as the long-range interaction between a line soliton and a y-periodic soliton, are also presented based on the Hirota formalism. By extending the multilinear variable separation approach to the fifthorder nonlinear evolution equation, various localized excitations are introduced, including solitoff, dromion, and an instanton excited by three resonant dromions. In addition to these localized excitations, the general fusion or fission type N-solitary wave solution is obtained, and the resonant Y-shaped soliton and the resonant T -type soliton interaction in shallow water are explored graphically.

Fusion and fission phenomena in a (2+1)-dimensional Sawada-Kotera type system

“…Figures 8(a) exhibits the three-dimensional lump structure of u at time t = 0. According to equation (33), the amplitude of u can be approximately calculated as 0.26, consistent with the presented figure.…”