Breather solutions of the discrete nonlinear Schrödinger equations with unbounded potentials

DOI10.1063/1.3036182zbMath1200.37072OpenAlexW1963554847MaRDI QIDQ3650878

Guoping Zhang

Publication date: 7 December 2009

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.3036182

zbMATH Keywords

wavesSchrödinger equationnonlinear equationseigenvalues and eigenfunctions

Mathematics Subject Classification ID

Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems (37K40) Lattice dynamics; integrable lattice equations (37K60)

Related Items (28)

Multiple solutions for Schrödinger lattice systems with asymptotically linear terms and perturbed terms ⋮ Initial value problem of the discrete nonlinear Schrödinger equation with complex potential ⋮ Multiple solutions of discrete Schrödinger equations with growing potentials ⋮ Homoclinic Solutions of Periodic Discrete Schrödinger Equations with Local Superquadratic Conditions ⋮ Discrete Schrödinger equations with sign-changing nonlinearities: infinitely many homoclinic solutions ⋮ Existence of exponentially and superexponentially spatially localized breather solutions for nonlinear klein–gordon lattices in ℤ^d, d ≥ 1 ⋮ Multibump solutions for discrete periodic nonlinear Schrödinger equations ⋮ Existence and multiplicity results of homoclinic solutions for the DNLS equations with unbounded potentials ⋮ Breathers of discrete one-dimensional nonlinear Schrödinger equations in inhomogeneous media ⋮ Homoclinic solutions for partial difference equations with mixed nonlinearities ⋮ Discrete nonlinear Schrödinger equations with superlinear nonlinearities ⋮ Discrete Schrödinger equations in the nonperiodic and superlinear cases: homoclinic solutions ⋮ Unnamed Item ⋮ Asymptotic behavior of the coupled nonlinear Schrödinger lattice system ⋮ Solitary waves of the Schrödinger lattice system with nonlinear hopping ⋮ Non-periodic Schrödinger lattice systems with perturbed and asymptotically linear terms: negative energy solutions ⋮ On standing wave solutions for discrete nonlinear Schrödinger equations ⋮ Standing wave solutions for discrete nonlinear Schrödinger equations with unbounded potentials and saturable nonlinearity ⋮ Homoclinic solutions for perturbed discrete Schrödinger systems in infinite lattices: sublinear and asymptotically linear cases ⋮ Multiplicity results of breathers for the discrete nonlinear Schrödinger equations with unbounded potentials ⋮ Localised time-periodic solutions of discrete nonlinear Klein-Gordon systems with convex on-site potentials ⋮ Standing waves for discrete nonlinear Schrödinger equations with nonperiodic bounded potentials ⋮ Multiple solutions for non-periodic Schrödinger lattice systems with perturbation and super-linear terms ⋮ Excitation threshold for the discrete coupled Schrödinger lattice system ⋮ HOMOCLINIC SOLUTIONS OF DISCRETE NONLINEAR SYSTEMS VIA VARIATIONAL METHOD ⋮ Breather solutions of the discrete nonlinear Schrödinger equations with sign changing nonlinearity ⋮ Ground State and Geometrically Distinct Solitons of Discrete Nonlinear Schrödinger Equations with Saturable Nonlinearities ⋮ Existence of exponentially spatially localized breather solutions for lattices of nonlinearly coupled particles: Schauder’s fixed point theorem approach

Cites Work

• Breathers in nonlinear lattices: existence, linear stability and quantization
• \(\mathcal H^s\) solutions for nonlinear Schrödinger equations with potentials superquadratic at infinity
• On a class of nonlinear Schrödinger equations
• On nontrivial solutions of a nonlinear Schrödinger equation with magnetic field
• Stability of standing waves for nonlinear Schrödinger equations with unbounded potentials
• Local smoothing property and Strichartz inequality for Schrödinger equations with potentials superquadratic at infinity
• Gap solitons in periodic discrete nonlinear Schrödinger equations. II: A generalized Nehari manifold approach
• Global existence and compact attractors for the discrete nonlinear Schrödinger equation
• Standing localized modes in nonlinear lattices
• Excitation thresholds for nonlinear localized modes on lattices
• A REMARK ON THE EXISTENCE OF BREATHER SOLUTIONS FOR THE DISCRETE NONLINEAR SCHRÖDINGER EQUATION IN INFINITE LATTICES: THE CASE OF SITE-DEPENDENT ANHARMONIC PARAMETERS
• Gap solitons in periodic discrete nonlinear Schrödinger equations
• On some discrete variational problems
• Smoothing property for Schrödinger equations with potential superquadratic at infinity.
• Unnamed Item

This page was built for publication: Breather solutions of the discrete nonlinear Schrödinger equations with unbounded potentials