The three-component defocusing nonlinear Schrödinger equation with nonzero boundary conditions

DOI10.1007/s00220-016-2626-7zbMath1365.35148arXiv1511.02885OpenAlexW2258711887MaRDI QIDQ728507

Barbara Prinari, Daniel K. Kraus, Gino Biondini

Publication date: 20 December 2016

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

Full work available at URL: https://arxiv.org/abs/1511.02885

zbMATH Keywords

inverse scattering transformexact soliton solutionsdark-bright solitonsanalytic eigenfunctionssymmetries of the eigenfunctionstensor approach

Mathematics Subject Classification ID

Scattering theory for PDEs (35P25) NLS equations (nonlinear Schrödinger equations) (35Q55) Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems (37K15) Soliton solutions (35C08)

Related Items

Focusing and defocusing mKdV equations with nonzero boundary conditions: inverse scattering transforms and soliton interactions, Imaginary eigenvalues of Zakharov-Shabat problems with non-zero background, Thermal solitons in nanotubes, Soliton and breather solutions for a fifth-order modified KdV equation with a nonzero background, The \(\bar{\partial}\)-dressing method applied to nonlinear defocusing Hirota equation with nonzero boundary conditions, Inverse scattering problem for the matrix modified Korteweg-de Vries equation with finite density type initial data, Darboux transformation for nonlinear Schrödinger type hierarchies, Soliton and breather solutions of the higher-order modified Korteweg-de Vries equation with constants background, The Riemann-Hilbert approach for the higher-order Gerdjikov-Ivanov equation, soliton interactions and position shift, Pointwise second order convergence of structure-preserving scheme for the triple-coupled nonlinear Schrödinger equations, Nonlinear Schrödinger equation with nonzero boundary conditions revisited: Dbar approach, Inverse scattering transform for nonlinear Schrödinger systems on a nontrivial background: a survey of classical results, new developments and future directions, Inverse scattering transform for the Gerdjikov-Ivanov equation with nonzero boundary conditions, Inverse scattering transformation for the \(N\)-component focusing nonlinear Schrödinger equation with nonzero boundary conditions, Rational solutions of multi‐component nonlinear Schrödinger equation and complex modified KdV equation, Inverse scattering transform and soliton solutions for square matrix nonlinear Schrödinger equations with non-zero boundary conditions, Kuznetsov-Ma solution and Akhmediev breather for TD equation, Inverse scattering transform for the nonlocal reverse space-time nonlinear Schrödinger equation, Inverse scattering transforms and soliton solutions of focusing and defocusing nonlocal mKdV equations with non-zero boundary conditions, Inverse scattering and \(N\)-triple-pole soliton and breather solutions of the focusing nonlinear Schrödinger hierarchy with nonzero boundary conditions, The n -component nonlinear Schrödinger equations: dark–bright mixed N - and high-order solitons and breathers, and dynamics, Pure soliton solutions of the nonlocal Kundu-nonlinear Schrödinger equation, Inverse scattering transform and multiple high-order pole solutions for the Gerdjikov-Ivanov equation under the zero/nonzero background, Reverse Space‐Time Nonlocal Sine‐Gordon/Sinh‐Gordon Equations with Nonzero Boundary Conditions, Inverse scattering transform for the coupled modified Korteweg-de Vries equation with nonzero boundary conditions, Riemann-Hilbert approach and \(N\)-soliton solutions of the generalized mixed nonlinear Schrödinger equation with nonzero boundary conditions, Semi-discrete integrable nonlinear Schrödinger system with background-controlled inter-site resonant coupling, Inverse Scattering Transform for the Defocusing Manakov System with Non-Parallel Boundary Conditions at Infinity

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Integrable nonlinear Schrödinger systems and their soliton dynamics
• Elastic and inelastic line-soliton solutions of the Kadomtsev-Petviashvili II equation
• Hamiltonian methods in the theory of solitons. Transl. from the Russian by A. G. Reyman
• Modulation instability: The beginning
• The nonlinear Schrödinger equation. Self-focusing and wave collapse
• Long-time asymptotics of solutions to the Cauchy problem for the defocusing nonlinear Schrödinger equation with finite-density initial data. II: Dark solitons on continua
• Inverse scattering transform for the defocusing nonlinear Schrödinger equation with fully asymmetric non-zero boundary conditions
• A steepest descent method for oscillatory Riemann-Hilbert problems. Asymptotics for the MKdV equation
• The Deodhar decomposition of the Grassmannian and the regularity of KP solitons
• 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 Multi-Component Nonlinear Schrödinger Equation with Nonzero Boundary Conditions
• The focusing Manakov system with nonzero boundary conditions
• Direct and inverse scattering transforms with arbitrary spectral singularities
• Soliton solutions of the Kadomtsev-Petviashvili II equation
• Inverse scattering transform for the vector nonlinear Schrödinger equation with nonvanishing boundary conditions
• Polarization interactions in multi-component defocusing media
• Classification of the line-soliton solutions of KPII
• Scattering and inverse scattering for first order systems
• Inverse scattering on the line
• The collisionless shock region for the long‐time behavior of solutions of the KdV equation
• On a family of solutions of the Kadomtsev–Petviashvili equation which also satisfy the Toda lattice hierarchy
• Nonlinear Waves, Solitons and Chaos
• Exponentially small asymptotics of solutions to the defocusing nonlinear Schrödinger equation: II
• Young diagrams and N-soliton solutions of the KP equation
• KP solitons, total positivity, and cluster algebras
• Inverse Scattering Transform for the Defocusing Manakov System with Nonzero Boundary Conditions
• The Integrable Nature of Modulational Instability
• 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
• Dark-bright soliton solutions with nontrivial polarization interactions for the three-component defocusing nonlinear Schrödinger equation with nonzero boundary conditions
• Integrals of nonlinear equations of evolution and solitary waves