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On Zero-Curvature Representations of Partial Differential Equations (1993)
| Citations: | 27 - 10 self |
BibTeX
@MISC{Marvan93onzero-curvature,
author = {M. Marvan and M. Marvan Opava},
title = {On Zero-Curvature Representations of Partial Differential Equations},
year = {1993}
}
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Abstract
. This paper concerns the problem of finding all possible zero-curvature representations of a given system of partial differential equations. A new computational procedure is proposed, designed to give complete answers. The procedure is applicable to non-overdetermined systems when the number m of independent variables is two, while for m ? 3 we prove a theorem of non-existence. The approach, inspired by A.M. Vinogradov's C-spectral sequence, is based on finding representatives of gauge equivalence classes. Keywords. Nonlinear partial differential equation, zero-curvature representation, linear pseudopotential, linear covering, AKNS formulation, diffiety, C-spectral sequence, gauge complex, gauge equivalence, jet comonad. MS classification numbers. 35A30, 58G05; 35G20, 18C15. Introduction Consider a system of partial differential equations f l (x i ; u k ; u k I ) = 0; (0.1) where x i , i = 1; : : : ; m are independent variables, u k 's are unknown functions, and u k I...
Keyphrases
partial differential equation zero-curvature representation c-spectral sequence independent variable non-overdetermined system a.m. vinogradov gauge complex linear covering unknown function possible zero-curvature representation gauge equivalence m classification number gauge equivalence class jet comonad akns formulation linear pseudopotential complete answer new computational procedure nonlinear partial differential equation
