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 consider ation: a nonlinear diatomic elastic chain, modulated nonlinear optical medi a, a diatomic easy-axis fi:ferromagnetic chain, and an easy-plane antiferro magnet in an external magnetic field. The main result of our work is a qual itative analysis of all kinds of small amplitude soliton excitations with f requencies lying in the gap and near the gap of the linear wave spectrum. W e also study the evolution of the system phase portrait and the bifurcation picture of the soliton solutions under changes of the medium parameters;. [S1063-651X(99)06408-9].