Initial boundary value problem for the mKdV equation on a finite interval.

DOI10.5802/aif.2056zbMath1137.35419arXivmath/0307194OpenAlexW2467569531MaRDI QIDQ1774069

Anne Boutet de Monvel-Berthier, Dimitry Shepelsky

Publication date: 29 April 2005

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0307194

zbMATH Keywords

initial-boundary value problemmodified Korteweg-de Vries equationfinite intervalglobal relationRiemann-Hilbert problem.

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Inverse problems involving ordinary differential equations (34A55) Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems (37K15) Riemann-Hilbert problems in context of PDEs (35Q15) Scattering theory, inverse scattering involving ordinary differential operators (34L25)

Related Items (18)

KdV equation in domains with moving boundaries ⋮ The unified transform method to the high-order nonlinear Schrödinger equation with periodic initial condition ⋮ The linear Lugiato-Lefever equation with forcing and nonzero periodic or nonperiodic boundary conditions ⋮ A Riemann–Hilbert Approach to Complex Sharma–Tasso–Olver Equation on Half Line ^* ⋮ The modified KdV equation on a finite interval. ⋮ Initial-boundary value problems for integrable evolution equations with \(3\times 3\) Lax pairs ⋮ Explicit Soliton Asymptotics for the Nonlinear Schrödinger Equation on the Half-Line ⋮ Boundary value problems for the stationary Kawahara equation ⋮ The Heat Equation in the Interior of an Equilateral Triangle ⋮ The Camassa-Holm equation on the half-line: a Riemann-Hilbert approach ⋮ Long time asymptotics of the Camassa-Holm equation on the half-line ⋮ A necessary and sufficient condition for the solvability of the nonlinear Schrödinger equation on a finite interval ⋮ Initial-boundary value problem for the spin-1 Gross-Pitaevskii system with a 4 × 4 Lax pair on a finite interval ⋮ Initial-Boundary Value Problems for the Coupled Nonlinear Schrödinger Equation on the Half-Line ⋮ Riemann-Hilbert formulation for the KdV equation on a finite interval ⋮ Asymptotic stage of modulation instability for the nonlocal nonlinear Schrödinger equation ⋮ The Korteweg–de Vries equation on the interval ⋮ The Camassa-Holm equation on the half-line

Cites Work

• Integration of nonlinear equations of mathematical physics by the method of inverse scattering. II
• A scheme for integrating the nonlinear equations of mathematical physics by the method of the inverse scattering problem. I
• Inverse scattering transform for systems with rational spectral dependence
• The modified KdV equation on a finite interval.
• Analysis of the global relation for the nonlinear Schrödinger equation on the half-line
• Integrable nonlinear evolution equations on the half-line
• On the integrability of linear and nonlinear partial differential equations
• Two–dimensional linear partial differential equations in a convex polygon
• The nonlinear Schrödinger equation on the interval
• A unified transform method for solving linear and certain nonlinear PDEs
• The Riemann–Hilbert Problem and Inverse Scattering
• THE mKdV EQUATION ON THE HALF-LINE
• The Linearization of the Initial-Boundary Value Problem of the Nonlinear Schrödinger Equation
• The nonlinear Schrödinger equation on the half-line

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