Asymptotic analysis of multi-valley dark soliton solutions in defocusing coupled Hirota equations

Abstract

We construct uniform expressions of such dark soliton solutions encompassing both single-valley and double-valley dark solitons for the defocusing coupled Hirota equation with high-order nonlinear effects utilizing the uniform Darboux transformation, in addition to proposing a sufficient condition for the existence of the above dark soliton solutions. Furthermore, the asymptotic analysis we perform reveals that collisions for single-valley dark solitons typically exhibit elastic behavior; however, collisions for double-valley dark solitons are generally inelastic. In light of this, we further propose a sufficient condition for the elastic collisions of double-valley dark soliton solutions. Our results offer valuable insights into the dynamics of dark soliton solutions in the defocusing coupled Hirota equation and can contribute to the advancement of studies in nonlinear optics.