Degenerate behaviors and decompositions of the two-soliton solution in the (1+1)-dimensional Ito equation

Abstract

In this paper, we investigate the degenerate behaviors and decompositions of two-soliton solution on the non-vanishing constant background for the (1+1)-dimensional Ito equation. By tuning the background constant, interaction phenomena of various types such as the elastic interaction of solitons, fission or fusion phenomena are presented. The degenerate two-soliton solutions which lead to a higher amplitude soliton in collisions of two solitons or describe the decay of a soliton into two new solitons are obtained. To better understand the nature of these interaction phenomena, we explore different decompositions to express the two-soliton solution as a sum of two functions. One of the function exhibits a special soliton excited by the collisions of two solitons, and the other describes the energy exchange of two solitons. Finally, under the module resonance of wave numbers, other types of the degenerate solutions of two solitons are derived and analyzed, such as the breather and rogue wave solutions.