Local conservation laws of second-order evolution equations
Roman O. Popovych, Anatoly M. Samoilenko
TL;DR
This paper classifies local conservation laws of second-order (1+1)-dimensional evolution equations, identifying possible dimensions of conservation law spaces and providing canonical forms for equations based on these dimensions.
Contribution
It extends Bryant and Griffiths' work by completely describing conservation laws of these equations up to contact equivalence, including canonical forms.
Findings
Conservation law space dimensions are 0, 1, 2, or infinity.
Canonical forms are provided for each nonzero dimension.
Complete classification up to contact equivalence.
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.
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