Discrete Solitons and Vortices in Nonlinear Schrödinger Lattices

Thursday, October 28, 2004 - 9:30am - 10:20am
EE/CS 3-180
Dmitry Pelinovsky (McMaster University)
We consider the discrete solitons and vortices bifurcating from the anti-continuum limit of the discrete nonlinear Schrodinger (NLS) lattice. The discrete soliton in the anti-continuum limit represents an arbitrary finite superposition of in-phase or anti-phase excited nodes, separated by an arbitrary sequence of empty nodes. The discrete vortices represent a finite set of excited nodes with non- phase shifts between the adjacent nodes.

By using stability analysis, we prove that the discrete solitons are all unstable near the anti-continuum limit, except for the solitons, which consist of alternating anti-phase excited nodes. We classify analytically and confirm numerically the number of unstable eigenvalues associated with each family of the discrete solitons.

By using Lyapunov-Schmidt reductions, we study existence and stability of symmetric, super-symmetric and asymmetric discrete vortices in simply-connected discrete contours on the plane.