Initial-boundary value problem for the spin-1 Gross-Pitaevskii system with a 4 × 4 Lax pair on a finite interval

DOI10.1063/1.5058722zbMath1421.37029arXiv1705.10665OpenAlexW2970642288MaRDI QIDQ5193209

Zhenya Yan

Publication date: 9 September 2019

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

Full work available at URL: https://arxiv.org/abs/1705.10665

zbMATH Keywords

initial-boundary value problemmatrix Riemann-Hilbert problemGross-Pitaevskii system

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions (37K20) Riemann-Hilbert problems in context of PDEs (35Q15) Initial-boundary value problems for systems of linear higher-order PDEs (35G46)

Related Items (10)

The initial boundary value problems for a nonlinear integrable equation with \(3 \times 3\) Lax pair on the finite interval ⋮ The initial-boundary value problems of the new two-component generalized Sasa-Satsuma equation with a \(4\times 4\) matrix Lax pair ⋮ Long-time asymptotics for the spin-1 Gross-Pitaevskii equation ⋮ The unified transform method to the high-order nonlinear Schrödinger equation with periodic initial condition ⋮ A coupled complex mKdV equation and its N-soliton solutions via the Riemann-Hilbert approach ⋮ On the Riemann–Hilbert problem of a generalized derivative nonlinear Schrödinger equation ⋮ Initial-boundary value problems for the two-component complex modified Korteweg-de Vries equation on the interval ⋮ Riemann-Hilbert problem for the fifth-order modified Korteweg–de Vries equation with the prescribed initial and boundary values ⋮ Riemann-Hilbert approach and \(N\)-soliton solutions for a new two-component Sasa-Satsuma equation ⋮ Long-time asymptotics for the focusing Hirota equation with non-zero boundary conditions at infinity via the Deift-Zhou approach

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Nonlocal general vector nonlinear Schrödinger equations: integrability, \(\mathcal{PT}\) symmetribility, and solutions
• Initial-boundary value problems for integrable evolution equations with \(3\times 3\) Lax pairs
• Integrable \(\mathcal{PT}\)-symmetric local and nonlocal vector nonlinear Schrödinger equations: a unified two-parameter model
• Exact stationary wave patterns in three coupled nonlinear Schrödinger/Gross-Pitaevskii equations
• The Degasperis-Procesi equation on the half-line
• The derivative nonlinear Schrödinger equation on the half-line
• An initial-boundary value problem for the sine-Gordon equation in laboratory coordinates
• An initial-boundary value problem for the Korteweg-de Vries equation
• The modified KdV equation on a finite interval.
• Analysis of the global relation for the nonlinear Schrödinger equation on the half-line
• The initial-boundary value problem for the Ostrovsky-Vakhnenko equation on the half-line
• Initial boundary value problem for the mKdV equation on a finite interval.
• Integrable nonlinear evolution equations on the half-line
• A novel hierarchy of two-family-parameter equations: local, nonlocal, and mixed-local-nonlocal vector nonlinear Schrödinger equations
• The Hirota equation: Darboux transform of the Riemann-Hilbert problem and higher-order rogue waves
• Inverse scattering transformation for generalized nonlinear Schrödinger equation
• A steepest descent method for oscillatory Riemann-Hilbert problems. Asymptotics for the MKdV equation
• The generalized Dirichlet to Neumann map for the KdV equation on the half-line
• Integrable nonlinear evolution equations on a finite interval
• On the integrability of linear and nonlinear partial differential equations
• Initial-Boundary Value Problem for Integrable Nonlinear Evolution Equation with 3 × 3 Lax Pairs on the Interval
• Initial-Boundary Value Problems for the Coupled Nonlinear Schrödinger Equation on the Half-Line
• The unified transform method for the Sasa–Satsuma equation on the half-line
• The unified method: I. Nonlinearizable problems on the half-line
• The unified method: II. NLS on the half-line witht-periodic boundary conditions
• The unified method: III. Nonlinearizable problems on the interval
• The nonlinear Schrödinger equation on the interval
• The Asymptotic Behavior of the Solution of Boundary Value Problems for the sine-Gordon Equation on a Finite Interval
• Inverse scattering transform for the vector nonlinear Schrödinger equation with nonvanishing boundary conditions
• A Unified Approach to Boundary Value Problems
• Initial-boundary-value problems for linear and integrable nonlinear dispersive partial differential equations
• A steepest descent method for oscillatory Riemann-Hilbert problems
• A unified transform method for solving linear and certain nonlinear PDEs
• Method for Solving the Korteweg-deVries Equation
• Scattering problem for the Zakharov-Shabat equations on the semi-axis
• Three-component Gross-Pitaevskii equations in the spin-1 Bose-Einstein condensate: Spin-rotation symmetry, matter-wave solutions, and dynamics
• An initial-boundary value problem for the integrable spin-1 Gross-Pitaevskii equations with a 4 × 4 Lax pair on the half-line
• The generalized Dirichlet-to-Neumann map for certain nonlinear evolution PDEs
• THE mKdV EQUATION ON THE HALF-LINE
• Semiclassical nonlinear Schrödinger on the half line
• The Linearization of the Initial-Boundary Value Problem of the Nonlinear Schrödinger Equation
• On the Nonlinear Schrödinger Equation on the Half Line with Homogeneous Robin Boundary Conditions
• Reverse Space‐Time Nonlocal Sine‐Gordon/Sinh‐Gordon Equations with Nonzero Boundary Conditions
• Advances in the study of boundary value problems for nonlinear integrable PDEs
• A Robust Inverse Scattering Transform for the Focusing Nonlinear Schrödinger Equation
• The nonlinear Schrödinger equation on the half-line
• Inverse scattering transform for the focusing nonlinear Schrödinger equation with nonzero boundary conditions
• Integrals of nonlinear equations of evolution and solitary waves

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