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The dynamics of two-component solitons is studied, analytically andnumerically, in the framework of a system of coupled extended nonlinearSchr\"odinger equations, which incorporate the cross-phase modulation,pseudo-stimulated-Raman-scattering (pseudo-SRS), cross-pseudo-SRS, andspatially inhomogeneous second-order dispersion (SOD). The system modelsco-propagation of electromagnetic waves with orthogonal polarizations inplasmas. It is shown that the soliton's wavenumber downshift, caused bypseudo-SRS, may be compensated by an upshift, induced by the inhomogeneous SOD,to produce stable stationary two-component solitons. The correspondingapproximate analytical solutions for stable solitons are found. Analyticalresults are well confirmed by their numerical counterparts. Further, theevolution of inputs composed of spatially even and odd components isinvestigated by means of systematic simulations, which reveal three differentoutcomes: formation of a breather which keeps opposite parities of thecomponents; splitting into a pair of separating vector solitons; and spreadingof the weak odd component into a small-amplitude pedestal with an embedded darksoliton.

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