  We report results of the study of solitons in a system of two
nonlinear-Schrodinger (NLS) equations coupled by the XPM interaction, which
models the co-propagation of two waves in metamaterials(MMs). The same model
applies to photonic crystals (PCs), as well as to ordinary optical fibers,
close to the zero-dispersion point. A peculiarity of the system is a small
positive or negative value of the relative group-velocity dispersion (GVD)
coefficient in one equation, assuming that the dispersion is anomalous in the
other. In contrast to earlier studied systems of nonlinearly coupled NLS
equations with equal GVD coefficients, which generate only simple single-peak
solitons, the present model gives rise to families of solitons with complex
shapes, which feature extended oscillatory tails and/or a double-peak structure
at the center. Regions of existence are identified for single- and double-peak
bimodal solitons, demonstrating a broad bistability in the system. Behind the
existence border, they degenerate into single-component solutions. Direct
simulations demonstrate stability of the solitons in the entire existence
regions. Effects of the group-velocity mismatch (GVM) and optical loss are
considered too. It is demonstrated that the solitons can be stabilized against
the GVM by means of the respective "management" scheme. Under the action of the
loss, complex shapes of the solitons degenerate into simple ones, but periodic
compensation of the loss supports the complexity.
