Decomposition of higher order equations of Monge-Ampere type
Exactly Solvable and Integrable Systems
2007-05-23 v1
Abstract
Given a function f(x, t), its fourth (symmetric) differential is a quartic form in dx, dt. It is well-known that any quartic form in two variables can be represented as a sum of three 4th powers of linear forms. The particular case of two 4th powers is characterized by the vanishing of a catalecticant determinant, which is a fourth order PDE for the function f. We demonstrate that this PDE decouples in a direct sum of two Monge-Ampere equations. A higher order generalization of this decomposition is also proposed.
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Cite
@article{arxiv.nlin/0205056,
title = {Decomposition of higher order equations of Monge-Ampere type},
author = {E. V. Ferapontov},
journal= {arXiv preprint arXiv:nlin/0205056},
year = {2007}
}
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6 pages