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On relation between potential and contact symmetries of evolution equations. (English) Zbl 1187.35026
Summary: We prove that any evolution equation, that can be written in the form of a conservation law, reduces to an evolution equation admitting the group of contact symmetries leaving the temporal variable invariant and vice versa. One of the consequences of this fact is that any evolution equation admitting the potential symmetries can be transformed into another evolution equation so that the potential symmetries map into contact symmetries of the latter. Based on this fact is out group approach to classification of evolution equations possessing nonlocal symmetries. We present several examples of classifications of second-order evolution equations admitting potential symmetries.{
©2009 American Institute of Physics}

MSC:
35G20 Nonlinear higher-order PDEs
35A30 Geometric theory, characteristics, transformations in context of PDEs
37K05 Hamiltonian structures, symmetries, variational principles, conservation laws (MSC2010)
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