Oliveri F. Symmetries, equivalence and decoupling of first order PDEs, talk at The Workshop on Integrable Nonlinear Equations, 18-24 October 2015, Mikulov, Czech Republic (abstract)

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Speaker: Francesco Oliveri

Title: Symmetries, equivalence and decoupling of first order PDEs

Abstract:
Systems of first order partial differential equations with the aim of identifying classes of equivalent ones (up to invertible point transformations) are considered.

In particular, necessary and sufficient conditions are established in order to map a general nonautonomous and nonhomogeneous quasilinear first order system of partial differential equations to a quasilinear autonomous and homogeneous one. Also, the necessary conditions in order to map a nonlinear first order system to quasilinear autonomous and homogeneous form are given. Both results are obtained in the framework of Lie group analysis of differential equations, and some examples are provided.

Finally, a general result concerned with the decoupling problem of a hyperbolic system of first order quasilinear partial differential equations is given.

Slides: Oliveri F. Symmetries, equivalence and decoupling of first order PDEs (presentation at The Workshop on Integrable Nonlinear Equations, 18-24 October 2015, Mikulov, Czech Republic).pdf