A note on critical points of integrals of soliton equations

I. M. Krichever, D. V. Zakharov

Research output: Contribution to journalArticlepeer-review

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Abstract

We consider the problem of extending the integrals of motion of soliton equations to the space of all finite-gap solutions. We consider the critical points of these integrals on the moduli space of Riemann surfaces with marked points and jets of local coordinates. We show that the solutions of the corresponding variational problem have an explicit description in terms of real-normalized differentials on the spectral curve. Such conditions have previously appeared in a number of problems of mathematical physics.

Original languageEnglish
Pages (from-to)15-35
Number of pages21
JournalAnalysis and Mathematical Physics
Volume1
Issue number1
DOIs
StatePublished - Mar 25 2011

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