DOI10.1111/sapm.12153zbMath1373.35281arXiv1610.02594OpenAlexW2531289303MaRDI QIDQ4592631
Mark J. Ablowitz, Ziad H. Musslimani
Publication date: 7 November 2017
Published in: Studies in Applied Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1610.02594
A novel Riemann–Hilbert approach via t-part spectral analysis for a physically significant nonlocal integrable nonlinear Schrödinger equation ⋮
Inverse scattering transforms for the nonlocal Hirota–Maxwell–Bloch system ⋮
Six wave interaction equations in finite-depth gravity waves with surface tension ⋮
Manakov system with parity symmetry on nonzero background and associated boundary value problems ⋮
Integrable nonlocal asymptotic reductions of physically significant nonlinear equations ⋮
Inverse scattering transforms for non-local reverse-space matrix non-linear Schrödinger equations ⋮
Self-Consistent Sources Extensions of Modified Differential-Difference KP Equation ⋮
Modified nonlinear Schrödinger models, 𝒞𝒫s𝒯d invariant N-bright solitons and infinite towers of anomalous charges ⋮
Integrable nonlocal derivative nonlinear Schrödinger equations ⋮
Nonlocal nonlinear Schrödinger equations and their soliton solutions ⋮
Effect of PT symmetry on nonlinear waves for three-wave interaction models in the quadratic nonlinear media ⋮
\((2+1)\)-dimensional AKNS \((-N)\) systems. II ⋮
Several reverse-time integrable nonlocal nonlinear equations: Rogue-wave solutions ⋮
Rogue waves of the nonlocal Davey–Stewartson I equation ⋮
Inverse scattering transform for a nonlocal derivative nonlinear Schrödinger equation ⋮
Solitary wave solutions and integrability for generalized nonlocal complex modified Korteweg-de Vries (cmKdV) equations ⋮
Dynamics of high-order solitons in the nonlocal nonlinear Schrödinger equations ⋮
Solutions to integrable space-time shifted nonlocal equations ⋮
On the non-chiral intermediate long wave equation ⋮
Alice-Bob systems, P^-T^-Ĉ symmetry invariant and symmetry breaking soliton solutions ⋮
Quasi-periodic wave solutions of the nonlocal coupled nonlinear Schrödinger equation ⋮
Binary Darboux transformation and new soliton solutions of the focusing nonlocal nonlinear Schrödinger equation ⋮
The nth-Darboux transformation and explicit solutions of the PT-symmetry second-type derivative nonlinear Schrödinger equation ⋮
Reduced nonlocal integrable mKdV equations of type (−λ, λ) and their exact soliton solutions ⋮
Bounded multi-soliton solutions and their asymptotic analysis for the reversal-time nonlocal nonlinear Schrödinger equation ⋮
Discrete solutions and interaction dynamics for coupled nonlocal discrete nonlinear Schrödinger equations in an inhomogeneous optical fiber ⋮
On the well-posedness of a nonlocal (two-place) FORQ equation via a two-component peakon system ⋮
Lagrangian nonlocal nonlinear Schrödinger equations ⋮
Soliton and breather solutions on the nonconstant background of the local and nonlocal Lakshmanan-Porsezian-Daniel equations by Bäcklund transformation ⋮
Darboux transformation and soliton solutions for a nonlocal two-component complex modified Korteweg-de Vries equation ⋮
Dbar‐approach to coupled nonlocal NLS equation and general nonlocal reduction ⋮
Reduced AKNS spectral problems and associated complex matrix integrable models ⋮
Integrable nonlocal nonlinear Schrödinger hierarchies of type \((-\lambda*,\lambda)\) and soliton solutions ⋮
Exact solutions and Darboux transformation for the reverse space-time nonlocal Lakshmanan-Porsezian-Daniel equation ⋮
Soliton solution and gauge equivalence for an integrable nonlocal complex modified Korteweg-de Vries equation ⋮
Solitons for the coupled matrix nonlinear Schrödinger-type equations and the related Schrödinger flow ⋮
On a coupled nonlocal nonlinear Schrödinger system ⋮
A generalized integrable lattice hierarchy related to the Ablowitz–Ladik lattice: Conservation law, Darboux transformation and exact solution ⋮
Large‐time asymptotics to the focusing nonlocal modified Kortweg‐de Vries equation with step‐like boundary conditions ⋮
Solutions and continuum limits to nonlocal discrete sine‐Gordon equations: Bilinearization reduction method ⋮
Some novel solitary wave characteristics for a generalized nonlocal nonlinear Hirota (GNNH) equation ⋮
Nonautonomous dynamics of local and nonlocal Fokas–Lenells models ⋮
Non-linear Schrödinger equation with time-dependent balanced loss-gain and space-time modulated non-linear interaction ⋮
Interaction of wave structure in the \(\mathcal{PT}\)-symmetric \((3+1)\)-dimensional nonlocal Mel'nikov equation and their applications ⋮
Integrable decomposition for the (2+1)-dimensional AKNS hierarchy and its applications ⋮
Bright soliton solutions to a nonlocal nonlinear Schrödinger equation of reverse-time type ⋮
Bi-Dbar-approach for a coupled shifted nonlocal dispersionless system ⋮
Long time asymptotic behavior for the nonlocal mKdV equation in solitonic space-time regions ⋮
Inverse scattering transform for the integrable fractional derivative nonlinear Schrödinger equation ⋮
The partial-rogue ripple solutions of nonlocal Kadomtsev-Petviashvili equation ⋮
New solutions of coupled nonlocal NLS and coupled nonlocal mKdV equations ⋮
Three-Wave Interaction Equations: Classical and Nonlocal ⋮
Non-Hermitian superintegrable systems ⋮
Binary Darboux transformation, solitons, periodic waves and modulation instability for a nonlocal Lakshmanan-Porsezian-Daniel equation ⋮
Multi-soliton solutions for the nonlocal Kundu-nonlinear Schrödinger equation with step-like initial data ⋮
Bright Soliton solutions to the nonlocal Manakov equations of reverse-space type ⋮
On the nonlocal third-order inhomogeneous Heisenberg spin system with self-consistent potential ⋮
Rational and semi-rational solutions to the nonlocal Davey-Stewartson III equation ⋮
Inverse scattering transform and dynamics of soliton solutions for nonlocal focusing modified Korteweg-de Vries equation ⋮
Riemann–Hilbert problems and N-soliton solutions of the nonlocal reverse space-time Chen–Lee–Liu equation ⋮
On \(\mathcal{PT}\)-symmetric semi-discrete coupled integrable dispersionless system ⋮
Inverse scattering transform for nonlinear Schrödinger systems on a nontrivial background: a survey of classical results, new developments and future directions ⋮
Dynamics of solitons and breathers on a periodic waves background in the nonlocal Mel'nikov equation ⋮
Darboux transformation and general soliton solutions for the reverse space-time nonlocal short pulse equation ⋮
\(N\)-fold Darboux transformation and exact solutions for the nonlocal Fokas-Lenells equation on the vanishing and plane wave backgrounds ⋮
A Study of Nonholonomic Deformations of Nonlocal Integrable Systems Belonging to the Nonlinear Schrödinger Family ⋮
Soliton solutions to constrained nonlocal integrable nonlinear Schrödinger hierarchies of type (−λ,λ) ⋮
Darboux transformation and soliton solutions of the nonlocal Heisenberg spin system with self-consistent potential ⋮
Discrete nonlocal nonlinear Schrödinger systems: Integrability, inverse scattering and solitons ⋮
Riemann–Hilbert approach to the focusing and defocusing nonlocal complex modified Korteweg–de Vries equation with step-like initial data ⋮
Explicit solutions from Darboux transformation for the two-component nonlocal Hirota and Maxwell–Bloch system ⋮
Elliptic‐ and hyperbolic‐function solutions of the nonlocal reverse‐time and reverse‐space‐time nonlinear Schrödinger equations ⋮
Multi-component AKNS systems ⋮
Multi-Breather, Rogue Wave and Multi-Bright-Dark Soliton Interaction of the (2+1)-Dimensional Nonlocal Fokas System ⋮
Integrable reductions of the multi-component Kaup-Newell equations ⋮
Long-time asymptotics for the integrable nonlocal nonlinear Schrödinger equation ⋮
Dynamics of soliton solutions of the nonlocal Kundu-nonlinear Schrödinger equation ⋮
The periodic Cauchy problem for PT-symmetric NLS, I: the first appearance of rogue waves, regular behavior or blow up at finite times ⋮
Solutions of the nonlocal (2+1)-D breaking solitons hierarchy and the negative order AKNS hierarchy ⋮
Multi-place physics and multi-place nonlocal systems ⋮
Inverse scattering and soliton solutions of nonlocal reverse-spacetime nonlinear Schrödinger equations ⋮
Finite-gap solutions of nonlocal equations in Ablowitz-Kaup-Newell-Segur hierarchy ⋮
General soliton solution to a nonlocal nonlinear Schrödinger equation with zero and nonzero boundary conditions ⋮
On the Spectral Stability of Standing Waves of Nonlocal $$\mathcal {P}\mathcal {T}$$ Symmetric Systems ⋮
General stationary solutions of the nonlocal nonlinear Schrödinger equation and their relevance to the PT-symmetric system ⋮
The massive Thirring system in the quarter plane ⋮
Reverse Space‐Time Nonlocal Sine‐Gordon/Sinh‐Gordon Equations with Nonzero Boundary Conditions ⋮
The finite-gap method and the periodic NLS Cauchy problem of anomalous waves for a finite number of unstable modes ⋮
Nonintegrable spatial discrete nonlocal nonlinear schrödinger equation ⋮
Long-Time Asymptotics for the Nonlocal MKdV Equation* ⋮
Inverse scattering transform for the complex reverse space-time nonlocal modified Korteweg-de Vries equation with nonzero boundary conditions and constant phase shift ⋮
Integrable nonlocal Hirota equations ⋮
GBDT and algebro-geometric approaches to explicit solutions and wave functions for nonlocal NLS ⋮
The Ablowitz-Ladik system on a graph ⋮
Explicit solutions to a nonlocal 2-component complex modified Korteweg-de Vries equation ⋮
Darboux transformation and multi-soliton solutions of local/nonlocal N-wave interactions ⋮
Inverse scattering transform for the nonlocal nonlinear Schrödinger equation with nonzero boundary conditions ⋮
Nonlocal gauge equivalence: Hirota versus extended continuous Heisenberg and Landau–Lifschitz equation ⋮
Soliton-like behaviour in non-integrable systems ⋮
An improved Hirota bilinear method and new application for a nonlocal integrable complex modified Korteweg-de Vries (MKdV) equation
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