Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2002-03-26
J. Phys. A: Math. Gen. 35 (2002) 10619-10628
Nonlinear Sciences
Exactly Solvable and Integrable Systems
12 pages; proof of Theorem 1 clarified; misprints corrected
Scientific paper
10.1088/0305-4470/35/49/309
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.
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