Bifurcation picture for gap solitons in nonlinear modulated systems

We investigate the problem of nonlinear wave propagation in periodic media. Four different classes of periodic nonlinear media are taken into consideration: a nonlinear diatomic elastic chain, modulated nonlinear optical media, a diatomic easy-axis ferromagnetic chain, and an easy-plane antiferromagnet in an external magnetic field. The main result of our work is a qualitative analysis of all kinds of small amplitude soliton excitations with frequencies lying in the gap and near the gap of the linear wave spectrum. We also study the evolution of the system phase portrait and the bifurcation picture of the soliton solutions under changes of the medium parameters.