2007/07/17 by F. Kh. Abdullaev, Yu. V. Bludov, S. V. Dmitriev +2 · 1 citation
Physics and Astronomy · #cond-mat.other #nlin.PS
paper · pdf · doi:10.1103/physreve.77.016604
published as PHYSICAL REVIEW E 77, 016604 (2008)
arxiv created 2007/07/17 · arxiv updated 2009/12/01
It is shown that the tight-binding approximation of the nonlinear Schrödinger 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 Schrödinger 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.