  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.
