Shock formation for general first-order strictly hyperbolic systems in one spatial dimension is self-similar and universal like the inviscid Burgers' equation, with an analytical formula for the self-similar solution.
John, Formation of singularities in one-dimensional nonlinear wave propagation , Commu- nications on Pure and Applied Mathematics, 27 (1974), pp
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Similarity Solutions of Shock Formation for First-order Strictly Hyperbolic Systems
Shock formation for general first-order strictly hyperbolic systems in one spatial dimension is self-similar and universal like the inviscid Burgers' equation, with an analytical formula for the self-similar solution.