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Nonclassical potential symmetry generators of differential equations. (English) Zbl 1013.35071
Summary: We determine the nonclassical potential symmetries for a number of equations that arise in the literature. A large number of these are obtained for some equations which only admit a single potential (classical) symmetry (e.g., the wave equation and the motion of waves through some medium). However, we show that some of the exact solutions invariant under the nonclassical potential symmetries are equivalent to known solutions but these solutions are not obtainable through the classical point or potential symmetries. It is shown that the Korteweg-de Vries equation does not admit nonclassical potential symmetries.
MSC:
35Q51Soliton-like equations
37K05Hamiltonian structures, symmetries, variational principles, conservation laws