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Symmetry and Integrability of Equations of Mathematical Physics − 2016
Vaycheslav M. Boyko (Institute of Mathematics, Kyiv)
Michael Kunzinger (Universität Wien, Wien, Austria)
Roman O. Popovych (Wolfgang Pauli Institute, Wien, Austria; Institute of Mathematics, Kyiv)
Singular reduction modules of differential equation
Abstract:
The notion of singular reduction modules, i.e., of singular modules of nonclassical (conditional) symmetry,
of differential equations is introduced.
It is shown that the derivation of nonclassical symmetries for differential equations
can be improved by an in-depth prior study of the associated singular modules of vector fields.
The form of differential functions and differential equations
possessing parameterized families of singular modules is described up to point transformations.
Singular cases of finding reduction modules are related to lowering the order of the corresponding reduced equations.
As examples, singular reduction modules of evolution equations and second-order quasi-linear equations are studied.
Reductions of differential equations to algebraic equations and to first-order ordinary differential equations are
considered in detail within the framework proposed and are related to previous no-go results on nonclassical symmetries.
This talk is based on the paper J. Math. Phys. 57 (2016), 101503, 34 pp., arXiv:1201.3223v3.
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