Generalized Neighbor-Interaction Models Induced by Nonlinear Lattices
arXiv:0707.2512 · doi:10.1103/PhysRevE.77.016604
Abstract
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 Schr{ö}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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- Vector solitons in nonlinear lattices
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- Dynamical localization of gap-solitons by time periodic forces
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- Dark Solitary Waves in a Class of Collisionally Inhomogeneous Bose-Einstein Condensates
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- Bifurcation of gap solitons in periodic potentials with a sign-varying nonlinearity coefficient
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