General soliton solution to a nonlocal nonlinear Schrödinger equation with zero and nonzero boundary conditions

DOI10.1088/1361-6544/aae031zbMath1406.37049arXiv1712.09172OpenAlexW3098086382MaRDI QIDQ4644664

Mark J. Ablowitz, Bao-Feng Feng, Xu-Dan Luo, Ziad H. Musslimani

Publication date: 8 January 2019

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1712.09172

zbMATH Keywords

nonlinear Schrödinger equationsoliton solutionsreduction methodKP hierarchyHirota's bilinear method

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Soliton equations (35Q51) Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems (37K15)

Related Items (73)

Three types of Darboux transformation and general soliton solutions for the space-shifted nonlocal \(\mathcal{PT}\) symmetric nonlinear Schrödinger equation ⋮ Type \(( - \lambda, - \lambda^\ast)\) reduced nonlocal integrable mKdV equations and their soliton solutions ⋮ Stability of trapped solutions of a nonlinear Schrödinger equation with a nonlocal nonlinear self-interaction potential ⋮ Integrable nonlocal asymptotic reductions of physically significant nonlinear equations ⋮ \(N\)-double poles solutions for nonlocal Hirota equation with nonzero boundary conditions using Riemann-Hilbert method and PINN algorithm ⋮ Riemann-Hilbert problems and soliton solutions of nonlocal reverse-time NLS hierarchies ⋮ \((2+1)\)-dimensional AKNS \((-N)\) systems. II ⋮ Solitons, breathers and rogue waves in the coupled nonlocal reverse-time nonlinear Schrödinger equations ⋮ Reduced non-local integrable NLS hierarchies by pairs of local and non-local constraints ⋮ Long-time asymptotics for the integrable nonlocal focusing nonlinear Schrödinger equation for a family of step-like initial data ⋮ \(P T\)-symmetric nonlocal Davey-Stewartson I equation: general lump-soliton solutions on a background of periodic line waves ⋮ Multiple bright soliton solutions of a reverse-space nonlocal nonlinear Schrödinger equation ⋮ Solitons, breathers and rational solutions for a (2+1)-dimensional dispersive long wave system ⋮ Bilinear equations in Darboux transformations by boson-fermion correspondence ⋮ Dynamics of high-order solitons in the nonlocal nonlinear Schrödinger equations ⋮ Solutions to integrable space-time shifted nonlocal equations ⋮ Binary Darboux transformation and new soliton solutions of the focusing nonlocal nonlinear Schrödinger equation ⋮ Global conservative solutions of the nonlocal NLS equation beyond blow-up ⋮ Bounded multi-soliton solutions and their asymptotic analysis for the reversal-time nonlocal nonlinear Schrödinger equation ⋮ Lagrangian nonlocal nonlinear Schrödinger equations ⋮ Dbar‐approach to coupled nonlocal NLS equation and general nonlocal reduction ⋮ Riemann-Hilbert approach to the focusing and defocusing nonlocal derivative nonlinear Schrödinger equation with step-like initial data ⋮ Transparent boundary conditions for the nonlocal nonlinear Schrödinger equation: a model for reflectionless propagation of PT-symmetric solitons ⋮ Interaction of wave structure in the \(\mathcal{PT}\)-symmetric \((3+1)\)-dimensional nonlocal Mel'nikov equation and their applications ⋮ A special two-dimensional lattice by Blaszak and Szum: solitons, breathers, lump solutions, and their interactions and dynamics ⋮ Bright soliton solutions to a nonlocal nonlinear Schrödinger equation of reverse-time type ⋮ Binary Darboux transformation, solitons, periodic waves and modulation instability for a nonlocal Lakshmanan-Porsezian-Daniel equation ⋮ Bright Soliton solutions to the nonlocal Manakov equations of reverse-space type ⋮ Rational and semi-rational solutions to the nonlocal Davey-Stewartson III equation ⋮ Nonlinear Schrödinger equation with nonzero boundary conditions revisited: Dbar approach ⋮ Multiple soliton solutions and symmetry analysis of a nonlocal coupled KP system ⋮ Dynamics of solitons and breathers on a periodic waves background in the nonlocal Mel'nikov equation ⋮ Periodic-background solutions of Kadomtsev-Petviashvili I equation ⋮ 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 ⋮ Solitons and symmetry reduction solutions of a nonlocal two‐mode Korteweg–de Vries equation ⋮ Multi-component AKNS systems ⋮ Multi-Breather, Rogue Wave and Multi-Bright-Dark Soliton Interaction of the (2+1)-Dimensional Nonlocal Fokas System ⋮ Multisoliton and general Wronskian solutions of a variable‐coefficient Korteweg–de Vries equation ⋮ The two-dimensional Leznov lattice equation and its various solutions ⋮ Collapse dynamics for two-dimensional space-time nonlocal nonlinear Schrödinger equations ⋮ Focusing nonlocal nonlinear Schrödinger equation with asymmetric boundary conditions: large-time behavior ⋮ Nonlocal hydrodynamic type of equations ⋮ Nonlocal coupled HI-MKdv systems ⋮ On the existence of solution, Lie symmetry analysis and conservation law of magnetohydrodynamic equations ⋮ Long-time asymptotics for the nonlocal nonlinear Schrödinger equation with step-like initial data ⋮ Discrete symmetries and nonlocal reductions ⋮ Nonlocal KdV equations ⋮ Mixed soliton solutions of the defocusing nonlocal nonlinear Schrödinger equation ⋮ Dynamics of soliton solutions of the nonlocal Kundu-nonlinear Schrödinger equation ⋮ Multi-place physics and multi-place nonlocal systems ⋮ Gram determinant solutions to nonlocal integrable discrete nonlinear Schrödinger equations via the pair reduction ⋮ Variational approximations of soliton dynamics in the Ablowitz-Musslimani nonlinear Schrödinger equation ⋮ Integrable space-time shifted nonlocal nonlinear equations ⋮ The Cauchy problem for nonlocal abstract Schrödinger equations and applications ⋮ Dynamics of lump-soliton solutions to the \(PT\)-symmetric nonlocal Fokas system ⋮ Soliton solutions to the reverse-time nonlocal Davey-Stewartson III equation ⋮ Families of nonsingular soliton solutions of a nonlocal Schrödinger-Boussinesq equation ⋮ Superposition of the coupled NLS and MKdV systems ⋮ Darboux transformations and exact solutions for the integrable nonlocal Lakshmanan-Porsezian-Daniel equation ⋮ On general solitons in the parity-time-symmetric defocusing nonlinear Schrödinger equation ⋮ General stationary solutions of the nonlocal nonlinear Schrödinger equation and their relevance to the PT-symmetric system ⋮ Higher-order interactional solutions and rogue wave pairs for the coupled Lakshmanan-Porsezian-Daniel equations ⋮ Rational and semi-rational solutions of the modified Kadomtsev-Petviashvili equation and the \((2+1)\)-dimensional Konopelchenko-Dubrovsky equation ⋮ Energy-sharing collisions and the dynamics of degenerate solitons in the nonlocal Manakov system ⋮ On general rogue waves in the parity-time-symmetric nonlinear Schrödinger equation ⋮ \(N\)-soliton solutions to the multi-component nonlocal Gerdjikov-Ivanov equation via Riemann-Hilbert problem with zero boundary conditions ⋮ Soliton solutions of the shifted nonlocal NLS and MKdV equations ⋮ Defocusing nonlocal nonlinear Schr\"odinger equation with step-like boundary conditions: long-time behavior for shifted initial data ⋮ Global Cauchy problems for the nonlocal (derivative) NLS in \(E_\sigma^s\) ⋮ Discrete nonlocal nonlinear Schrödinger equation on graphs: dynamics of PT-symmetric solitons in discrete networks

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Breathers and rogue waves for a third order nonlocal partial differential equation by a bilinear transformation
• \(N\)-soliton solution for an integrable nonlocal discrete focusing nonlinear Schrödinger equation
• Integrable \(\mathcal{PT}\)-symmetric local and nonlocal vector nonlinear Schrödinger equations: a unified two-parameter model
• Solitons and infinite dimensional Lie algebras
• On a structure of the explicit solutions to the Davey-Stewartson equations
• Solutions of the nonlocal nonlinear Schrödinger hierarchy via reduction
• Nonlocal Fordy-Kulish equations on symmetric spaces
• Nonstandard bilinearization of \(\mathcal{PT}\)-invariant nonlocal nonlinear Schrödinger equation: bright soliton solutions
• On a nonlocal modified Korteweg-de Vries equation: integrability, Darboux transformation and soliton solutions
• Solitons and dynamics for a general integrable nonlocal coupled nonlinear Schrödinger equation
• Darboux transformations and global solutions for a nonlocal derivative nonlinear Schrödinger equation
• The \(N\)-wave equations with \(\mathcal{PT}\) symmetry
• Soliton solutions of an integrable nonlocal modified Korteweg-de Vries equation through inverse scattering transform
• On solutions of constrained KP equations
• Integrable multidimensional versions of the nonlocal nonlinear Schrödinger equation
• Inverse scattering transform for the integrable nonlocal nonlinear Schrödinger equation
• Inverse Scattering Transform for the Focusing Ablowitz-Ladik System with Nonzero Boundary Conditions
• Nonlocal nonlinear Schrödinger equation and its discrete version: Soliton solutions and gauge equivalence
• General N-Dark-Dark Solitons in the Coupled Nonlinear Schrödinger Equations
• Nonlinear-Evolution Equations of Physical Significance
• 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
• Complete integrability of nonlocal nonlinear Schrödinger equation
• Inverse scattering transform for the nonlocal nonlinear Schrödinger equation with nonzero boundary conditions
• The focusing Manakov system with nonzero boundary conditions
• Inverse scattering transform for the vector nonlinear Schrödinger equation with nonvanishing boundary conditions
• Method for Generating Discrete Soliton Equation. III
• Discrete nonlinear Schrodinger equation under nonvanishing boundary conditions
• Nonlinear differential−difference equations
• Nonlinear differential–difference equations and Fourier analysis
• The Inverse Scattering Transform‐Fourier Analysis for Nonlinear Problems
• KP symmetry reductions and a generalized constraint
• 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
• On the focusing non-linear Schrödinger equation with non-zero boundary conditions and double poles
• Transformations between Nonlocal and Local Integrable Equations
• Nonlocal nonlinear Schrödinger equations and their soliton solutions
• Integrable Nonlocal Nonlinear Equations
• Soliton solution and gauge equivalence for an integrable nonlocal complex modified Korteweg-de Vries equation
• Rational and Semirational Solutions of the Nonlocal Davey–Stewartson Equations
• Rational solutions of the KP hierarchy and the dynamics of their poles. II. Construction of the degenerate polynomial solutions
• Reverse Space‐Time Nonlocal Sine‐Gordon/Sinh‐Gordon Equations with Nonzero Boundary Conditions
• Inverse Scattering Transform for the Discrete Focusing Nonlinear Schrödinger Equation with Nonvanishing Boundary Conditions
• Periodic and hyperbolic soliton solutions of a number of nonlocal nonlinear equations
• Inverse Scattering Transform for the Defocusing Manakov System with Nonzero Boundary Conditions
• Solutions of Nonlocal Equations Reduced from the AKNS Hierarchy
• Inverse scattering transform for the focusing nonlinear Schrödinger equation with nonzero boundary conditions
• Wave Instabilities
• Inverse scattering transform for the integrable discrete nonlinear Schrödinger equation with nonvanishing boundary conditions

This page was built for publication: General soliton solution to a nonlocal nonlinear Schrödinger equation with zero and nonzero boundary conditions