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Hamiltonian and algebro-geometric integrals of stationary equations of KdV type

Published online by Cambridge University Press:  24 October 2008

George Wilson
George Wilson
Affiliation:
Mathematical Institute, Oxford
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Extract

In this paper we shall generalize a theorem of Bogoyavl'enskii (2) showing the equivalence of two apparently different families of integrals of the ‘higher stationary Korteweg–de Vries (KdV)’ equations. We recall that the KdV equations form a hierarchy of evolution equations

for an unknown function u(x, t). The equations can be written in ‘Lax form’ (7)

where L is the Schrödinger operator (δ2/δx2) + u, and P+ runs through all the (ordinary) differential operators such that the commutator on the right of (1·1) has order zero.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 87 , Issue 2 , March 1980 , pp. 295 - 305
Copyright
Copyright © Cambridge Philosophical Society 1980

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References

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