# Vector solitons in coupled nonlinear Schr\"odinger equations with spatial stimulated scattering and inhomogeneous dispersion

## TL;DR

This paper investigates the behavior of two-component vector solitons in coupled nonlinear Schrödinger equations with spatial inhomogeneity and stimulated scattering effects, revealing conditions for stable solitons and their dynamic evolution.

## Contribution

It introduces analytical and numerical analysis of stable two-component solitons in a system with inhomogeneous dispersion and pseudo-SRS effects, which models electromagnetic wave propagation in plasmas.

## Key findings

- Stable two-component solitons can be achieved by balancing pseudo-SRS downshift with inhomogeneous SOD.
- Analytical solutions for stable solitons are derived and confirmed numerically.
- Different evolution scenarios include breather formation, soliton splitting, and spreading of odd components.

## Abstract

The dynamics of two-component solitons is studied, analytically and numerically, in the framework of a system of coupled extended nonlinear Schr\"odinger equations, which incorporate the cross-phase modulation, pseudo-stimulated-Raman-scattering (pseudo-SRS), cross-pseudo-SRS, and spatially inhomogeneous second-order dispersion (SOD). The system models co-propagation of electromagnetic waves with orthogonal polarizations in plasmas. It is shown that the soliton's wavenumber downshift, caused by pseudo-SRS, may be compensated by an upshift, induced by the inhomogeneous SOD, to produce stable stationary two-component solitons. The corresponding approximate analytical solutions for stable solitons are found. Analytical results are well confirmed by their numerical counterparts. Further, the evolution of inputs composed of spatially even and odd components is investigated by means of systematic simulations, which reveal three different outcomes: formation of a breather which keeps opposite parities of the components; splitting into a pair of separating vector solitons; and spreading of the weak odd component into a small-amplitude pedestal with an embedded dark soliton.

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Source: https://tomesphere.com/paper/1705.06722