Degenerate soliton solutions and their dynamics in the nonlocal Manakov system: I Symmetry preserving and symmetry breaking solutions

TL;DR

This paper constructs and analyzes degenerate soliton solutions in the nonlocal Manakov system, exploring both symmetry-preserving and symmetry-breaking cases, and discusses their key features and dynamics.

Contribution

It introduces a nonstandard bilinear method to derive degenerate soliton solutions, including symmetry-breaking cases, expanding understanding of nonlocal integrable systems.

Findings

Degenerate soliton solutions preserve or break PT-symmetry.

Solutions include both degenerate and nondegenerate cases.

Salient features of the solitons are discussed.

Abstract

In this paper, we construct degenerate soliton solutions (which preserve $\cal{PT}$-symmetry/break $\cal{PT}$-symmetry) to the nonlocal Manakov system through a nonstandard bilinear procedure. Here by degenerate we mean the solitons that are present in both the modes which propagate with same velocity. The degenerate nonlocal soliton solution is constructed after briefly indicating the form of nondegenerate one-soliton solution. To derive these soliton solutions, we simultaneously solve the nonlocal Manakov equation and a pair of coupled equations that arise from the zero curvature condition. The later consideration yields general soliton solution which agrees with the solutions that are already reported in the literature under certain specific parametric choice. We also discuss the salient features associated with the obtained degenerate soliton solutions.