Nondegenerate Solitons and their Collisions in Manakov System

TL;DR

This paper explores nondegenerate vector solitons in the Manakov system, deriving exact solutions, analyzing their diverse profiles and collision behaviors, and revealing their relation to previously known energy exchanging solitons.

Contribution

It introduces a comprehensive analysis of nondegenerate vector solitons, deriving explicit solutions, and examining their collision dynamics and profile variations, expanding understanding beyond degenerate cases.

Findings

Nondegenerate solitons can have double-hump, flat-top, and single-hump profiles.

Shape preserving and shape altering collisions are possible under certain conditions.

Degenerate solitons are a special case of the nondegenerate solitons.

Abstract

Recently, we have shown that the Manakov equation can admit a more general class of nondegenerate vector solitons, which can undergo collision without any intensity redistribution in general among the modes, associated with distinct wave numbers, besides the already known energy exchanging solitons corresponding to identical wave numbers. In the present comprehensive paper, we discuss in detail the various special features of the reported nondegenerate vector solitons. To bring out these details, we derive the exact forms of such vector one-, two- and three-soliton solutions through Hirota bilinear method and they are rewritten in more compact forms using Gram determinants. The presence of distinct wave numbers allows the nondegenerate fundamental soliton to admit various profiles such as double-hump, flat-top and single-hump structures. We explain the formation of double-hump structure in the fundamental soliton when the relative velocity of the two modes tends to zero. More critical analysis shows that the nondegenerate fundamental solitons can undergo shape preserving as well as shape altering collisions under appropriate conditions. The shape changing collision occurs between the modes of nondegenerate solitons when the parameters are fixed suitably. Then we observe the coexistence of degenerate and nondegenerate solitons when the wave numbers are restricted appropriately in the obtained two-soliton solution. In such a situation we find the degenerate soliton induces shape changing behavior of nondegenerate soliton during the collision process. By performing suitable asymptotic analysis we analyze the consequences that occur in each of the collision scenario. Finally we point out that the previously known class of energy exchanging vector bright solitons, with identical wave numbers, turns out to be a special case of the newly derived nondegenerate solitons.