Exact Solutions of the Saturable Discrete Nonlinear Schrodinger Equation

Abstract

Exact solutions to a nonlinear Schr{ö}dinger lattice with a saturable nonlinearity are reported. For finite lattices we find two different standing-wave-like solutions, and for an infinite lattice we find a localized soliton-like solution. The existence requirements and stability of these solutions are discussed, and we find that our solutions are linearly stable in most cases. We also show that the effective Peierls-Nabarro barrier potential is nonzero thereby indicating that this discrete model is quite likely nonintegrable.

References in corpus (4)

• Discrete Solitons and Breathers with Dilute Bose-Einstein Condensates
• Cyclic Identities Involving Jacobi Elliptic Functions
• Cyclic Identities Involving Jacobi Elliptic Functions. II
• Local Identities Involving Jacobi Elliptic Functions

Cited by in corpus (38)

• Periodic and Hyperbolic Soliton Solutions of a Number of Nonlocal PT-Symmetric Nonlinear Equations
• Multistable Solitons in the Cubic-Quintic Discrete Nonlinear Schrödinger Equation
• Discrete soliton mobility in two-dimensional waveguide arrays with saturable nonlinearity
• Discrete flat-band solitons in the Kagome lattice
• Moving solitons in the discrete nonlinear Schrödinger equation
• Multistable Solitons in Higher-Dimensional Cubic-Quintic Nonlinear Schroedinger Lattices
• Statistical Mechanics of Systems with Negative Temperature
• Elliptic general analytic solutions
• Exact solitary wave solutions for a discrete $\lambda {\varphi }^4$ field theory in 1+1 dimensions
• Linear Superposition for a Large Number of Nonlinear Equations
• Compactification tuning for nonlinear localized modes in sawtooth lattices
• Discrete soliton collisions in a waveguide array with saturable nonlinearity
• Mobility of solitons in one-dimensional lattices with the cubic-quintic nonlinearity
• Standing lattice solitons in the discrete NLS equation with saturation
• Discrete Nonlinear Schrodinger Equations Free of the Peierls-Nabarro Potential
• Superposition of Elliptic Functions as Solutions For a Large Number of Nonlinear Equations
• Discrete Nonlinear Schrodinger Equations with arbitrarily high order nonlinearities
• Nonlinear localized modes in dipolar Bose-Einstein condensates in optical lattices
• Mobility of high-power solitons in saturable nonlinear photonic lattices
• Peierls-Nabarro energy surfaces and directional mobility of discrete solitons in two-dimensional saturable nonlinear Schrödinger lattices
• Variational approximations for travelling solitons in a discrete nonlinear Schrödinger equation
• Comparative Study of Different Discretizations of the ${\varphi }^4$ Model
• High-speed kinks in a generalized discrete ${\varphi }^4$ model
• Exact static solutions to a translationally invariant discrete ${\varphi }^4$ model
• Domain Wall and Periodic Solutions of Coupled phi4 Models in an External Field
• Stability, mobility and power currents in a two-dimensional model for waveguide arrays with nonlinear coupling
• Statistical Mechanics of a Discrete Schrödinger Equation with Saturable Nonlinearity
• Homoclinic standing waves in focussing DNLS equations --Variational approach via constrained optimization
• Exact Moving and Stationary Solutions of a Generalized Discrete Nonlinear Schrodinger Equation
• Dynamic and Static Excitations of a Classical Discrete Anisotropic Heisenberg Ferromagnetic Spin Chain
• Exact Solutions of a Non-Polynomially Nonlinear Schrodinger Equation
• Doubly periodic waves of a discrete nonlinear Schrödinger system with saturable nonlinearity
• Multi-stable regime and intermediate solutions in a nonlinear saturable coupler
• Staggered and short period solutions of the Saturable Discrete Nonlinear Schrödinger Equation
• The exact solutions and their linear stability analysis for 2-dimensional Ablowitz-Ladik equation
• Exact Solutions of the Two-Dimensional Discrete Nonlinear Schrödinger Equation with Saturable Nonlinearity
• Breather mobility and the PN potential: Brief review and recent progress
• Multiscale reduction of discrete nonlinear Schroedinger equations