Discrete solitons of the focusing Ablowitz-Ladik equation with nonzero boundary conditions via inverse scattering

DOI10.1063/1.4961160zbMath1351.35190OpenAlexW2510325160MaRDI QIDQ2820931

Barbara Prinari

Publication date: 12 September 2016

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

Full work available at URL: https://doi.org/10.1063/1.4961160

zbMATH Keywords

inverse scattering transformsoliton solutionsfocusing nonlinear Schrödinger equationAblowitz-Ladik equation

Mathematics Subject Classification ID

Inverse problems for PDEs (35R30) NLS equations (nonlinear Schrödinger equations) (35Q55) Inverse scattering problems in quantum theory (81U40) Soliton equations (35Q51) Soliton solutions (35C08)

Related Items (12)

Neural networks enforcing physical symmetries in nonlinear dynamical lattices: the case example of the Ablowitz-Ladik model ⋮ General rogue wave solution to the discrete nonlinear Schrödinger equation ⋮ Long-time asymptotics for a mixed nonlinear Schrödinger equation with the Schwartz initial data ⋮ \(l^2\)-Sobolev space bijectivity of the scattering-inverse scattering transforms related to defocusing Ablowitz-Ladik systems ⋮ Riemann–Hilbert approach for discrete sine‐Gordon equation with simple and double poles ⋮ The effect of loss/gain and Hamiltonian perturbations of the Ablowitz—Ladik lattice on the recurrence of periodic anomalous waves ⋮ Modulation instability, periodic anomalous wave recurrence, and blow up in the Ablowitz–Ladik lattices ⋮ Inverse scattering transform for nonlinear Schrödinger systems on a nontrivial background: a survey of classical results, new developments and future directions ⋮ Double-pole solutions in the modified nonlinear Schrödinger equation ⋮ Kuznetsov-Ma solution and Akhmediev breather for TD equation ⋮ The robust inverse scattering method for focusing Ablowitz-Ladik equation on the non-vanishing background ⋮ Riemann-Hilbert approach to the modified nonlinear Schrödinger equation with non-vanishing asymptotic boundary conditions

Cites Work

• Unnamed Item
• Unnamed Item
• Modulation instability and periodic solutions of the nonlinear Schrödinger equation
• Waves that appear from nowhere and disappear without a trace
• Modulation instability: The beginning
• Exact integration of nonlinear Schrödinger equation
• Inverse Scattering Method for the Nonlinear Evolution Equations under Nonvanishing Conditions
• Inverse Scattering Transform for the Focusing Ablowitz-Ladik System with Nonzero Boundary Conditions
• The inverse scattering transform for the focusing nonlinear Schrödinger equation with asymmetric boundary conditions
• The Inverse Scattering Transform for the Defocusing Nonlinear Schrödinger Equations with Nonzero Boundary Conditions
• Inverse Scattering Transform for the Focusing Nonlinear Schrödinger Equation with a One-Sided Non-Zero Boundary Condition
• Water waves, nonlinear Schrödinger equations and their solutions
• Complete integrability for a discrete Heisenberg chain
• The Dirac inverse spectral transform: Kinks and boomerons
• Non-self-adjoint Zakharov–Shabat operator with a potential of the finite asymptotic values. I. Direct spectral and scattering problems
• Discrete nonlinear Schrodinger equation under nonvanishing boundary conditions
• Nonlinear differential–difference equations and Fourier analysis
• The Perturbed Plane-Wave Solutions of the Cubic Schrödinger Equation
• General rogue waves in the focusing and defocusing Ablowitz–Ladik equations
• Inverse Scattering Transform for the Discrete Focusing Nonlinear Schrödinger Equation with Nonvanishing Boundary Conditions
• Inverse scattering transform for the focusing nonlinear Schrödinger equation with nonzero boundary conditions
• On the Spectrum of the Dirac Operator and the Existence of Discrete Eigenvalues for the Defocusing Nonlinear Schrödinger Equation
• The disintegration of wave trains on deep water Part 1. Theory
• Inverse scattering transform for the integrable discrete nonlinear Schrödinger equation with nonvanishing boundary conditions
• Soliton Solutions for Discrete Hirota Equation. II

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