Abstract
This chapter presents a criterion of involutive systems of partial differential equations. The criterion is based on the concept of formal extended Pfaffian systems with fixed independent variables which introduced in this chapter. The system is involutive if and only if the formal extended of the system coincides with the usual extended. This criterion was proved that the order of nontrivial contact transformations allowed by the involutive system of partial differential equations cannot exceed the order of this system. This criterion can also be useful for constructing computer algorithms for reducing a system of differential equations to an involutive form.
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Talyshev, A.A. (2021). On Involutive Systems of Partial Differential Equations. In: Luo, A.C.J., Gazizov, R.K. (eds) Symmetries and Applications of Differential Equations. Nonlinear Physical Science. Springer, Singapore. https://doi.org/10.1007/978-981-16-4683-6_7
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DOI: https://doi.org/10.1007/978-981-16-4683-6_7
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