Local conservation laws of second-order evolution equations

Abstract

Generalizing results by Bryant and Griffiths [Duke Math. J., 1995, V.78, 531-676], we completely describe local conservation laws of second-order (1+1)-dimensional evolution equations up to contact equivalence. The possible dimensions of spaces of conservation laws prove to be 0, 1, 2 and infinity. The canonical forms of equations with respect to contact equivalence are found for all nonzero dimensions of spaces of conservation laws.

11 pages, minor corrections

References in corpus (3)

• Conservation Laws and Potential Symmetries of Linear Parabolic Equations
• Hierarchy of Conservation Laws of Diffusion--Convection Equations
• Reducibility of zero curvature representations with application to recursion operators

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