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JOURNALS // Zapiski Nauchnykh Seminarov POMI // Archive

Zap. Nauchn. Sem. POMI, 1996 Volume 235, Pages 245–259 (Mi znsl3652)

Nonlinear evolution equations and their stationary reductions

Allan P. Fordy, Simon Harris

University of Leeds, Leeds, UK

Abstract: In recent years there have been many papers on stationary flows of integrable nonlinear evolution equations and their Hamiltonian properties. In particular there have been some results concerning the reversal of the roles of $x$ and $t$, resulting in PDEs which are Hamiltonian and give the usual stationary Poisson brackets in the reduced case. To date the results have been rather ad hoc and disparate. In this brief report we give a systematic construction of these $x-t$ reversed equations and their Hamiltonian properties, using their isospectral properties. We illustrate our approach with examples from the KdV hierarchy. Bibl. 5 titles.

UDC: 517.9

Received: 20.10.1995

Language: English


 English version:
Journal of Mathematical Sciences (New York), 1999, 94:4, 1600–1610

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© Steklov Math. Inst. of RAS, 2025