Exact analytical soliton solutions of $N$-component coupled nonlinear Schr\"{o}dinger equations with arbitrary nonlinear parameters

TL;DR

This paper derives exact vector soliton solutions for N-component coupled nonlinear Schrödinger equations without restrictive parameter constraints, broadening potential experimental observations in optics and condensates.

Contribution

It removes previous nonlinear parameter constraints, providing explicit solutions and existence conditions for vector solitons in coupled systems.

Findings

Explicit exact soliton solutions derived

Existence conditions for solutions established

Applications discussed in experimental regimes

Abstract

Exact analytical soliton solutions play an important role in soliton fields. Soliton solutions were obtained with some special constraints on the nonlinear parameters in nonlinear coupled systems, but they usually do not holds in real physical systems. We successfully release all usual constrain conditions on nonlinear parameters for exact analytical vector soliton solutions in $N$-component coupled nonlinear Schr\"{o}dinger equations. The exact soliton solutions and their existence condition are given explicitly. Applications of these results are discussed in several present experimental parameters regimes. The results would motivate experiments to observe more novel vector solitons in nonlinear optical fibers, Bose-Einstein condensates, and other nonlinear coupled systems.