The association of non-local symmetries with conservation laws: applications to the heat and Burgers’ equations. (English) Zbl 1084.35075

Summary: We extend the definition of the association of symmetries of partial differential equations with conservation laws to the nonlocal case. It is shown that if a conservation law is associated to a symmetry, a part of its equivalence class is also associated to that symmetry. Applications to the linear heat equation, the potential Burgers’ equation and Burgers’ equation are given.


35Q53 KdV equations (Korteweg-de Vries equations)
35K05 Heat equation
37K05 Hamiltonian structures, symmetries, variational principles, conservation laws (MSC2010)
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