Discrete Nonlinear Schrodinger Equations with arbitrarily high order nonlinearities

Abstract

A class of discrete nonlinear Schrodinger equations with arbitrarily high order nonlinearities is introduced. These equations are derived from the same Hamiltonian using different Poisson brackets and include as particular cases the saturable discrete nonlinear Schrodinger equation and the Ablowitz-Ladik equation. As a common property, these equations possess three kinds of exact analytical stationary solutions for which the Peierls-Nabarro barrier is zero. Several properties of these solutions, including stability, discrete breathers and moving solutions, are investigated.

References in corpus (15)

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Cited by in corpus (13)

• Dark soliton oscillations in Bose-Einstein condensates with multi-body interactions
• Comparative Study of Different Discretizations of the ${\varphi }^4$ Model
• High-speed kinks in a generalized discrete ${\varphi }^4$ model
• Domain Wall and Periodic Solutions of Coupled phi4 Models in an External Field
• Exact static solutions to a translationally invariant discrete ${\varphi }^4$ model
• Dynamic and Static Excitations of a Classical Discrete Anisotropic Heisenberg Ferromagnetic Spin Chain
• Intrinsic Localized Modes in a Nonlinear Electrical Lattice with Saturable Nonlinearity
• Exact Moving and Stationary Solutions of a Generalized Discrete Nonlinear Schrodinger Equation
• Solitons in strongly driven discrete nonlinear Schrödinger-type models
• Doubly periodic waves of a discrete nonlinear Schrödinger system with saturable nonlinearity
• Thermalization in the one-dimensional Salerno model lattice
• Exact Solutions of the Two-Dimensional Discrete Nonlinear Schrödinger Equation with Saturable Nonlinearity
• Mobility of localized beams in non-homogeneous photonic lattices