Several Localized Waves Induced by Linear Interference between a Nonlinear Plane Wave and Bright Solitons

TL;DR

This paper explores how linear interference between a nonlinear plane wave and bright solitons in a Bose-Einstein condensate creates various localized wave structures, with detailed conditions and interaction behaviors analyzed.

Contribution

It introduces explicit conditions for multiple localized wave formations due to linear interference, expanding understanding of wave interactions in nonlinear quantum systems.

Findings

Multiple localized wave structures identified, including anti-dark, W-shaped, and multi-peak solitons.

Interaction analysis shows inelastic collisions for solitons and elastic for breathers.

Profiles depend on relative phase, with solitons influenced by phase, breathers not.

Abstract

We investigate linear interference effects between a nonlinear plane wave and bright solitons, which are admitted by pair-transition coupled two-component Bose-Einstein condensate. We demonstrate the interference effects can induce several localized waves possessing distinctive wave structures, mainly including anti-dark soliton, W-shaped soliton, multi-peak soliton, Kuznetsov-Ma like breather, and multi-peak breather. Especially, the explicit conditions for them are clarified by a phase diagram based on the linear interference properties. Furthermore, the interactions between these localized waves are discussed. The detailed analysis indicate that soliton-soliton interaction induced phase shift brings the collision between these localized waves be inelastic for soliton involving collision, and be elastic for breathers. These characters come from that the profile of solitons depend on relative phase between bright soliton and plane wave, and the profile of breathers do not depend on the relative phase. These results would motivate more discussions on linear interference between other nonlinear waves. Especially, the solitons or breathers obtained here are not related with modulational instability. The underlying reasons are discussed in detail.