Algebraic-geometrical methods in the theory of integrable equations and their perturbations

DOI10.1007/BF00994629zbMath0840.35095OpenAlexW4241521229MaRDI QIDQ1896391

I. M. Krichever

Publication date: 4 July 1996

Published in: Acta Applicandae Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00994629

zbMATH Keywords

exact solutionsquasiperiodic solutionsKadomtsev-Petviashvili equationsfinite-gap solutionsRiemann's theta-function

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) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Elliptic curves (14H52) Solutions to PDEs in closed form (35C05)

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\((X,\psi)\) duality and enhanced KdV on a Riemann surface, The space of equivariant harmonic tori in the 3-sphere, The whitham equations revisited, Riemann-Hilbert problem associated to Frobenius manifold structures on Hurwitz spaces: Irregular singularity, Nonlinear quantum-dynamical system based on the Kadomtsev-Petviashvili II equation, Some survey remarks on Whitham theory and Em duality, Whitham deformations and the space of harmonic tori in S3, Algebraic solutions of the multicomponent KP hierarchy

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