Dynamics of Solitons in Spectral Gaps and Near the Gap's Edge

Dynamics of Solitons in Spectral Gaps and Near the Gap's Edge

Boaz Ilan
Applied Mathematics
University of California at Merced

Bound state solutions (solitons) of nonlinear Schrödinger equations with a potential are investigated. Rigorous theory, asymptotic analysis, and direct computations elucidate the nature and magnitude of soliton instabilities in the semi-infinite spectral gap (first Brillouin zone). This is demonstrated with periodic, quasi-crystal, and other lattice-type structures. When the propagation constant bifurcates from the edge of the gap the soliton turns into a modulated Bloch-like wave. The ensuing structure and implications to collapse dynamics are investigated in detail.