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Marí Beffa, Gloria

The theory of differential invariants and KdV Hamiltonian evolutions. (English) Zbl 1053.37046

Bull. Soc. Math. Fr. 127, No. 3, 363-391 (1999).
Summary: The author proves that the second KdV Hamiltonian evolution associated to \(\text{SL}\) can be viewed as the most general evolution of projective curves, invariant under the \(\text{SL}\)-projective action on \(\mathbb RP^{n-1}\), provided that certain integrability conditions are satisfied. This way, she establishes a very close relationship between the theory of geometric invariance and KdV Hamiltonian evolutions. This relationship has been conjectured by A. González-López, R. H. Heredero and the author [J. Math. Phys. 38, No. 11, 5720–5738 (1997; Zbl 0892.58037)].

Cited in 11 Documents

MSC:

37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems
53A55 Differential invariants (local theory), geometric objects

Keywords:

differential invariants; projective action; invariant evolutions of projective curves; KdV Hamiltonian evolutions; Adler-Gel’fand-Dikii Poisson brackets

Citations:

Zbl 0892.58037
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References:

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