RT Journal Article
T1 Invariant differential equations and the Adler-Gel'fand-Dikii bracket
A1 González López, Artemio
A1 Hernández Heredero, Rafael
A1 Beffa, Gloria Marí
AB 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 .
PB American Institute of Physics
SN 0022-2488
YR 1997
FD 1997-11
LK https://hdl.handle.net/20.500.14352/59725
UL https://hdl.handle.net/20.500.14352/59725
LA eng
NO © 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.
NO DGES
DS Docta Complutense
RD 10 abr 2025