Simplest potential conservation laws of linear evolution equations

Abstract

Every simplest potential conservation law of any (1+1)-dimensional linear evolution equation of even order proves induced by a local conservation law of the same equation. This claim is true also for linear simplest potential conservation laws of (1+1)-dimensional linear evolution equations of odd order, which are related to linear potential systems. We also derive an effective criterion for checking whether a quadratic conservation law of a simplest linear potential system is a purely potential conservation law of a (1+1)-dimensional linear evolution equation of odd order.

12 pages, contribution to the Proceedings of 5th Workshop "Group Analysis of Differential Equations and Integrable Systems" (June 6-10, 2010, Protaras, Cyprus); v2: minor corrections

References in corpus (5)

• Conservation Laws and Potential Symmetries of Linear Parabolic Equations
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Cited by in corpus (1)

• Group classification of linear evolution equations