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- W2719949116 abstract "The notion of differential-invariant solutions is a generalization notions of invariant and partially invariant solutions. It is closely related to the notion of automorphic systems. The system of differential equations is called an automorphic with respect to the Lie group (G), if there is any solution of this system is obtained one fixed solution through action group of transformations (G). In contrast to the invariant and partially invariant, making use of the differential-invariant solutions has not yet received equally widespread. In this chapter, it is shown that if Lie group (G) is a finite-dimensional group, then some finite (as a rule of zero order) prolongation of a automorphic system is completely integrable system. This fact is useful in constructing automorphic systems. Also, we prove theorems on integration and on order reducing for the automorphic systems." @default.
- W2719949116 created "2017-06-30" @default.
- W2719949116 creator A5028853426 @default.
- W2719949116 date "2017-06-25" @default.
- W2719949116 modified "2023-09-27" @default.
- W2719949116 title "Automorphic Systems and Differential-Invariant Solutions" @default.
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- W2719949116 doi "https://doi.org/10.1007/978-3-319-58062-3_12" @default.
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