Invariant differential equations and the Adler-Gel'fand-Dikii bracket



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González López, Artemio and Hernández Heredero, Rafael and Beffa, Gloria Marí (1997) Invariant differential equations and the Adler-Gel'fand-Dikii bracket. Journal of mathematical physics, 38 (11). pp. 5720-5738. ISSN 0022-2488

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In this paper we find an explicit formula for the most general vector evolution of curves on RPn−1 invariant under the projective action of SL(n, R). When this formula is applied to the projectivization of solution curves of scalar Lax operators with periodic coefficients, one obtains a corresponding evolution in the space of such operators. We conjecture that this evolution is identical to the second KdV Hamiltonian evolution under appropriate conditions. These conditions give a Hamiltonian interpretation of general vector differential invariants for the projective action of SL(n, R), namely, the SL(n, R) invariant evolution can be written so that a general vector differential invariant corresponds to the Hamiltonian pseudo-differential operator. We find common coordinates and simplify both evolutions so that one can attempt to prove the equivalence for arbitrary n .

Item Type:Article
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© 1997 American Institute of Physics.
A.G-L. and R.H.H. would like to acknowledge the partial financial support of the DGES under Grant No. PB95-0401.

Uncontrolled Keywords:Korteweg-devries type
Subjects:Sciences > Physics > Physics-Mathematical models
Sciences > Physics > Mathematical physics
ID Code:32862
Deposited On:26 Aug 2015 11:19
Last Modified:10 Dec 2018 15:10

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