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Algebraic—Geometrical Methods in the Theory of Integrable Equations and Their Perturbations

In: KdV ’95

Author

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  • I. Krichever

    (Landau Institute for Theoretical Physics)

Abstract

The year of 1995 is not merely the centenary of the Korteweg—de Vries equation which we celebrate at this conference. It is also the year of the ‘majority’ of the finite-gap or algebraic—geometrical theory of integration of nonlinear equations — one of the most important components of the branch of modern mathematical physics, which is called the theory of integrable systems or the soliton theory. The main goal of this paper is to present the key points of the finite-gap theory and some of its applications. Part of its applications is directly related to the KdV equation, while a part of them lies beyond the framework of not only this particular equation but the theory of soliton equations in general. Corresponding examples refer to the string theory and topological field theory models. Not aspiring to be exhaustive, they manifest versatility of the methods, the origin of which would be forever related to the magic words: Korteweg—de Vries Equation.

Suggested Citation

  • I. Krichever, 1995. "Algebraic—Geometrical Methods in the Theory of Integrable Equations and Their Perturbations," Springer Books, in: Michiel Hazewinkel & Hans W. Capel & Eduard M. de Jager (ed.), KdV ’95, pages 93-125, Springer.
    • Handle: RePEc:spr:sprchp:978-94-011-0017-5_6
    DOI: 10.1007/978-94-011-0017-5_6
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