Nonlocal reductions of the Ablowitz-Ladik equation (Q1716177)

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scientific article

Language	Label	Description	Also known as
English	Nonlocal reductions of the Ablowitz-Ladik equation	scientific article

Statements

scholarly article

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Nonlocal reductions of the Ablowitz-Ladik equation (English)

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Erdal Karapınar

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Theoretical and Mathematical Physics

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publication date

4 February 2019

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full work available at URL

https://arxiv.org/abs/1711.08419

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zbMATH Keywords

integrable system

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soliton

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PT symmetry

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nonlocal reduction

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Riemann-Hilbert problem

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MaRDI profile type

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Integrable Hamiltonian hierarchies. Spectral and geometric methods

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Inverse-scattering problem for a system of differential equations

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Evolution equations associated with the discrete analog of the matrix Schrödinger spectral problem solvable by the inverse spectral transform

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Generalised Fourier transforms for the soliton equations. Gauge-covariant formulation

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A scheme for integrating the nonlinear equations of mathematical physics by the method of the inverse scattering problem. I

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Fordy-Kulish model and spinor Bose-Einstein condensate

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\(N\)-wave interactions related to simple Lie algebras. \(\mathbb{Z}_2\)-reductions and soliton solutions

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Polynomial bundles and generalised Fourier transforms for integrable equations on A.III-type symmetric spaces

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On the Caudrey-Beals-Coifman System and the Gauge Group Action

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Nonlinear Schrödinger equations and simple Lie algebras

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The reduction problem and the inverse scattering method

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On Mikhailov's reduction group

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Nonlinear differential−difference equations

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Nonlinear differential–difference equations and Fourier analysis

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A Nonlinear Difference Scheme and Inverse Scattering

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Discrete Vector Solitons: Composite Solitons, Yang–Baxter Maps and Computation

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Inverse scattering transform for the integrable discrete nonlinear Schrödinger equation with nonvanishing boundary conditions

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The Ablowitz–Ladik system with linearizable boundary conditions

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Expansions over the ‘‘squared’’ solutions and difference evolution equations

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Complete integrability for a discrete Heisenberg chain

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On discretizations of the vector nonlinear Schrödinger equation

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The nonabelian Toda lattice: Discrete analogue of the matrix Schrödinger spectral problem

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Integrable semi-discretization of the coupled nonlinear Schrödinger equations

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Discrete nonlinear Schrodinger equation under nonvanishing boundary conditions

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Functional representation of the Ablowitz-Ladik hierarchy

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Complete integrability of nonlocal nonlinear Schrödinger equation

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Inverse scattering transform for the integrable nonlocal nonlinear Schrödinger equation

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Review article: \(\mathcal {PT}\)-symmetric deformations of integrable models

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Real Spectra in Non-Hermitian Hamiltonians Having<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="bold-script">P</mml:mi><mml:mi mathvariant="bold-script">T</mml:mi></mml:math>Symmetry

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Pseudo-Hermiticity versus PT symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian

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Pseudo-Hermiticity and generalized <i>PT</i>- and <i>CPT</i>-symmetries

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The \(N\)-wave equations with \(\mathcal{PT}\) symmetry

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Multi-component NLS models on symmetric spaces: spectral properties versus representations theory

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Reductions of<i>N</i>-wave interactions related to low-rank simple Lie algebras: I. ℤ<sub>2</sub>-reductions

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The generating operator for the n \(\times n\) linear system

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A dressing method in mathematical physics.

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Inverse scattering transform for the nonlocal nonlinear Schrödinger equation with nonzero boundary conditions

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Inverse scattering transform for the focusing Ablowitz-Ladik system with nonzero boundary conditions

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On integrable wave interactions and Lax pairs on symmetric spaces

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Nonlocal Fordy-Kulish equations on symmetric spaces

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Identifiers

zbMATH Open document ID

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10.1134/S0040577918100021

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Mathematics Subject Classification ID

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zbMATH DE Number

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Sitelinks

Mathematics(1 entry)

mardi Publication:1716177

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