The modified KdV equation on a finite interval.

DOI10.1016/j.crma.2003.09.009zbMath1044.35080OpenAlexW2083945692MaRDI QIDQ1415582

Anne Boutet de Monvel-Berthier, Dimitry Shepelsky

Publication date: 9 December 2003

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.crma.2003.09.009

zbMATH Keywords

initial-boundary value problemspectral functionsmKdV equationmatrix Riemann-Hilbert problem

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) KdV equations (Korteweg-de Vries equations) (35Q53) Riemann-Hilbert problems in context of PDEs (35Q15)

Related Items (16)

Initial-boundary value problems for the two-component complex modified Korteweg-de Vries equation on the interval ⋮ The linear Lugiato-Lefever equation with forcing and nonzero periodic or nonperiodic boundary conditions ⋮ The solution of the global relation for the derivative nonlinear Schrödinger equation on the half-line ⋮ Initial-boundary value problems for integrable evolution equations with \(3\times 3\) Lax pairs ⋮ Computing the Solution of the m-Korteweg-de Vries Equation on Turing Machines ⋮ Initial boundary value problem for the mKdV equation on a finite interval. ⋮ The generalized Dirichlet-to-Neumann map for certain nonlinear evolution PDEs ⋮ Initial-boundary value problem for the spin-1 Gross-Pitaevskii system with a 4 × 4 Lax pair on a finite interval ⋮ The Camassa-Holm equation on the half-line with linearizable boundary condition ⋮ Nonlinear Fourier Transforms and the mKdV Equation in the Quarter Plane ⋮ The hyperbolic Ernst–Maxwell equations in a triangular domain ⋮ Initial-Boundary Value Problems for the Coupled Nonlinear Schrödinger Equation on the Half-Line ⋮ Linearizable boundary value problems for the elliptic sine-Gordon and the elliptic Ernst equations ⋮ Riemann-Hilbert formulation for the KdV equation on a finite interval ⋮ Initial-boundary value problem for the two-component Gerdjikov-Ivanov equation on the interval ⋮ The Korteweg–de Vries equation on the interval

Cites Work

• Initial boundary value problem for the mKdV equation on a finite interval.
• Integrable nonlinear evolution equations on the half-line
• On the integrability of linear and nonlinear partial differential equations
• The nonlinear Schrödinger equation on the interval
• A unified transform method for solving linear and certain nonlinear PDEs
• THE mKdV EQUATION ON THE HALF-LINE

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