Invariant solutions and nonlinear wave propagation

Physics

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Scientific paper

We consider quasi-linear hyperbolic systems in the one-dimensional case, which are invariant with respect to infinitesimal groups of transformations and we study the propagation of weak discontinuities across a similarity line. We are led to suitable compatibility conditions which are certainly fulfilled in the case of invariance with respect to the stretching group. The results are applied to the equation governing the deformations of an infinite axi-symmetric elastic-plastic medium.

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