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

• Published in: Communications in nonlinear science & numerical simulation Vol. 54; pp. 13 - 20
• Main Authors: Gromov, E.M., Malomed, B.A., Tyutin, V.V.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01-01-2018; Elsevier Science Ltd
• Subjects: Computer simulation; Coupled extended nonlinear Schrödinger equations; Dispersion; Electromagnetic radiation; Inhomogeneous Dispersion; Mathematical models; Nonlinear equations; Phase modulation; Plasmas (physics); Propagation; Scattering; Schrodinger equation; Solitary waves; Spatial stimulated Raman scattering; Vector Solitons; Wave propagation; Wavelengths; Spatial stimulated Raman scattering; Coupled extended nonlinear Schrödinger equations; Inhomogeneous Dispersion; Vector Solitons
• ISSN: 1007-5704; 1878-7274
• DOI: 10.1016/j.cnsns.2017.05.012

•Vector solitons in coupled extended nonlinear Schrödinger equations are studied.•We consider media with a pseudo-Raman-scattering and inhomogeneous dispersion.•Analytical and numerical methods are employed.•Soliton solutions are found and investigated.•Evolution of inputs with opposite parities of the two components is explored.
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.