Inverse Scattering Transform for the Focusing Ablowitz-Ladik System with Nonzero Boundary Conditions

DOI10.1111/sapm.12103zbMath1346.35174OpenAlexW2281677761MaRDI QIDQ2816383

Federica Vitale, Barbara Prinari

Publication date: 22 August 2016

Published in: Studies in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1111/sapm.12103

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) NLS equations (nonlinear Schrödinger equations) (35Q55) Soliton equations (35Q51)

Related Items (12)

Riemann-Hilbert approach to TD equation with nonzero boundary condition ⋮ \(N\)-bright-dark soliton solution to a semi-discrete vector nonlinear Schrödinger equation ⋮ 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 ⋮ Discrete nonlocal nonlinear Schrödinger systems: Integrability, inverse scattering and solitons ⋮ Periodic and localized wave patterns for coupled Ablowitz-Ladik systems with negative cross phase modulation ⋮ Nonlocal reductions of the Ablowitz-Ladik equation ⋮ General soliton solution to a nonlocal nonlinear Schrödinger equation with zero and nonzero boundary conditions ⋮ Preface: Mark J. Ablowitz, nonlinear waves and integrable systems. Part I ⋮ Discrete solitons of the focusing Ablowitz-Ladik equation with nonzero boundary conditions via inverse scattering ⋮ The robust inverse scattering method for focusing Ablowitz-Ladik equation on the non-vanishing background

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