2 research outputs found
Conservation laws for multidimensional systems and related linear algebra problems
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 solve over an
arbitrary field the matrix equations SA=A^tS and SA=-A^tS for a quadratic
matrix A and its transpose A^t, which may be of independent interest.Comment: 12 pages; proof of Theorem 1 clarified; misprints correcte