Author: Sergei IGONIN
We consider multidimensional systems of PDEs of generalized evolution
form with t-derivatives of arbitrary order on the left-hand
side and with the right-hand side dependent on lower order
t-derivatives and arbitrary space derivatives.
For such systems
we find an explicit necessary condition for existence of higher
conservation laws in terms of the system's symbol.
For systems that violate this condition we give an effective upper
bound on the order of conservation laws.
Using this result, we completely describe
conservation laws for viscous transonic equations,
for the Brusselator model, and the Belousov-Zhabotinskii system.
To achieve this, we determine the conditions for a quadratic
matrix A with entries from an arbitrary field to be similar
(conjugate) to its transpose At or to the matrix -At,
which is of independent interest.
11 pages, LaTeX-2e (AmSLaTeX).
To compile source files (.tex) one needs the title page style files titlatex.tex.