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González López, Artemio and Hernández Heredero, Rafael and Beffa, Gloria Marí (1997) Invariant differential equations and the AdlerGel'fandDikii bracket. Journal of mathematical physics, 38 (11). pp. 57205738. ISSN 00222488

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

http://scitation.aip.org  Publisher 
http://arxiv.org/abs/hepth/9603199  Organisation 
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 pseudodifferential operator. We find common coordinates and simplify both evolutions so that one can attempt to prove the equivalence for arbitrary n .
Item Type:  Article 

Additional Information:  © 1997 American Institute of Physics. 
Uncontrolled Keywords:  Kortewegdevries type 
Subjects:  Sciences > Physics > PhysicsMathematical 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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