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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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Official URL: http://dx.doi.org/10.1063/1.532162

## Abstract

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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Additional Information: | © 1997 American Institute of Physics. |

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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