Vector solitons in coupled nonlinear Schrödinger equations with spatial stimulated scattering and inhomogeneous dispersion

Communications in Nonlinear Science and Numerical Simulation. 2018. Vol. 54. P. 13–20.

Громов Е. М., Malomed B. A., Тютин В. В.

The dynamics of two-component solitons is studied, analytically and numerically, in the framework of a system of coupled extended nonlinear Schrödinger 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.

Ключевые слова: векторные солитоны, spatial stimulated Raman scattering, неоднородная дисперсия, Coupled Extended Nonlinear Schrödinger Equations, Inhomogeneous Dispersion, Vector Solitons, Связанные расширенные нелинейные уравнения Шредингера, Псевдо индуцированное рассеяние Рамана