Nonlinear Sciences – Pattern Formation and Solitons
Scientific paper
2006-10-27
Nonlinear Sciences
Pattern Formation and Solitons
14 pages, 10 figures
Scientific paper
10.1103/PhysRevE.74.066606
While fundamental-mode discrete solitons have been demonstrated with both self-focusing and defocusing nonlinearity, high-order-mode localized states in waveguide lattices have been studied thus far only for the self-focusing case. In this paper, the existence and stability regimes of dipole, quadrupole and vortex soliton structures in two-dimensional lattices induced with a defocusing nonlinearity are examined by the theoretical and numerical analysis of a generic envelope nonlinear lattice model. In particular, we find that the stability of such high-order-mode solitons is quite different from that with self-focusing nonlinearity. As a simple example, a dipole (``twisted'') mode soliton which may be stable in the focusing case becomes unstable in the defocusing regime. Our results may be relevant to other two-dimensional defocusing periodic nonlinear systems such as Bose-Einstein condensates with a positive scattering length trapped in optical lattices.
Chen Zai-Zhang
Kevrekidis Panagiotis G.
Susanto Hadi
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