The Riemann boundary value problem on closed Riemann surfaces and integrable systems

DOI10.1016/0167-2789(87)90065-0zbMath0605.30043OpenAlexW2058413379MaRDI QIDQ1084231

Yu. L. Rodin

Publication date: 1987

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0167-2789(87)90065-0

zbMATH Keywords

Schrödinger equationRiemann problemKorteweg-de Vries equationRiemann-Roch theoremAbelian differentials

Mathematics Subject Classification ID

Boundary value problems in the complex plane (30E25) Schrödinger operator, Schrödinger equation (35J10) Research exposition (monographs, survey articles) pertaining to functions of a complex variable (30-02) Scattering theory of linear operators (47A40) Differentials on Riemann surfaces (30F30) Generalizations of Bers and Vekua type (pseudoanalytic, (p)-analytic, etc.) (30G20)

Related Items (7)

The Riemann problem and matrix-valued potentials with a convergent Baker-Akhiezer function ⋮ Fast-decaying potentials on the finite-gap background and the \(\overline {\partial}\)-problem on the Riemann surfaces ⋮ Perturbation theory based on the Riemann problem for the Landau-Lifshitz equation ⋮ Solvability of the inverse scattering problem for the Landau-Lifshitz equation. I ⋮ Riemann problem method for generalized Heisenberg equation ⋮ Rapidly decreasing potentials on a background of finite-zone potentials and the \(\bar\partial\)-problem on Riemann surfaces ⋮ Loops in \(\mathrm{SU}(2)\), Riemann surfaces, and factorization. I.

Cites Work

• Expansion of invariant operators
• The reduction problem and the inverse scattering method
• Minimal factorization of matrix and operator functions
• Convolution equations and linear systems
• Inverse problem for periodic finite-zoned potentials in the theory of scattering
• Theta functions on Riemann surfaces
• The Riemann-Hilbert problem for finite riemann surfaces
• Scattering and inverse scattering for first order systems
• On a new non-local formulation of water waves
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