Localized and periodic exact solutions to the nonlinear Schrodinger equation with spatially modulated parameters: Linear and nonlinear lattices

Abstract

Using similarity transformations we construct explicit solutions of the nonlinear Schrodinger equation with linear and nonlinear periodic potentials. We present explicit forms of spatially localized and periodic solutions, and study their properties. We put our results in the framework of the exploited perturbation techniques and discuss their implications on the properties of associated linear periodic potentials and on the possibilities of stabilization of gap solitons using polychromatic lattices.

17 pages, 5 figures

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Cited by in corpus (10)

• Solitons in nonlinear lattices
• Solitons in combined linear and nonlinear lattice potentials
• The inverse problem for the Gross - Pitaevskii equation
• Solitary waves in coupled nonlinear Schrodinger equations with spatially inhomogeneous nonlinearities
• Solitons supported by singular spatial modulation of the Kerr nonlinearity
• Stable two-dimensional solitons supported by radially inhomogeneous self-focusing nonlinearity
• Quasi-one-dimensional Bose-Einstein condensates in nonlinear lattices
• Exactly solvable Gross-Pitaevskii type equations
• Effects of the third-order dispersion on continuous waves in complex potentials
• Exact solutions for periodic and solitary matter waves in nonlinear lattices