Generalized Neighbor-Interaction Models Induced by Nonlinear Lattices

Details Generalized Neighbor-Interaction Models Induced by Nonlinear Lattices Generalized Neighbor-Interaction Models Induced by Nonlinear Lattices

2007-07-17

arxiv.org/abs/0707.2512v1

PHYSICAL REVIEW E 77, 016604 (2008)

Physics

Condensed Matter

Other Condensed Matter

Scientific paper

10.1103/PhysRevE.77.016604

It is shown that the tight-binding approximation of the nonlinear Schr\"odinger equation with a periodic linear potential and periodic in space nonlinearity coefficient gives rise to a number of nonlinear lattices with complex, both linear and nonlinear, neighbor interactions. The obtained lattices present non-standard possibilities, among which we mention a quasi-linear regime, where the pulse dynamics obeys essentially the linear Schr{\"o}dinger equation. We analyze the properties of such models both in connection with their modulational stability, as well as in regard to the existence and stability of their localized solitary wave solutions.

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