Singularities of multivalued solutions of nonlinear differential equations, and nonlinear phenomena
It is shown how the geometrical theory of nonlinear partial differential equations and the theory of singularities of maps can be used to obtain a general scheme for constructing shock waves from smooth multivalued solutions. This scheme is illustrated by examples from gas dynamics, mechanics, acoustics and thermodynamics. The paper is popularly written and includes an introductive exposition of multivalued solutions, symmetries and conservation laws of differential equations on manifolds.
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