On the formation of shocks of electromagnetic plane waves in non-linear crystals

DOI10.1063/1.4960044zbMath1348.78014arXiv1505.04101OpenAlexW1715386332MaRDI QIDQ2820872

Daniel Raoul Perez, Demetrios Christodoulou

Publication date: 12 September 2016

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1505.04101

zbMATH Keywords

electromagnetic wavesshock wave solutionscharacteristic coordinatesnonlinear crystalsquasi-linear hyperbolic PDEs

Mathematics Subject Classification ID

Electromagnetic effects in solid mechanics (74F15) Lasers, masers, optical bistability, nonlinear optics (78A60) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Waves and radiation in optics and electromagnetic theory (78A40) Second-order semilinear hyperbolic equations (35L71) Initial value problems for first-order hyperbolic equations (35L03)

Related Items (11)

Low regularity ill-posedness for non-strictly hyperbolic systems in three dimensions ⋮ Stable shock formation for nearly simple outgoing plane symmetric waves ⋮ Shock formation for 2\(D\) quasilinear wave systems featuring multiple speeds: blowup for the fastest wave, with non-trivial interactions up to the singularity ⋮ On the formation of shock for quasilinear wave equations with weak intensity pulse ⋮ Exact solutions and singularities of an X-point collapse in Hall magnetohydrodynamics ⋮ Low regularity ill-posedness for elastic waves driven by shock formation ⋮ The relativistic Euler equations: ESI notes on their geo-analytic structures and implications for shocks in 1D and multi-dimensions ⋮ Shock formation in solutions to the \(2D\) compressible Euler equations in the presence of non-zero vorticity ⋮ Stable ODE-type blowup for some quasilinear wave equations with derivative-quadratic nonlinearities ⋮ Self-similarity in the singularity formation for the unsteady Prandtl's equations and related problems ⋮ Multidimensional nonlinear geometric optics for transport operators with applications to stable shock formation

Cites Work

• Unnamed Item
• On the formation of shocks for quasilinear wave equations
• The formation of shocks in 3-dimensional fluids.
• Lectures on nonlinear hyperbolic differential equations
• Compressible Flow and Euler's Equations
• Formation of singularities in one-dimensional nonlinear wave propagation
• The Action Principle and Partial Differential Equations. (AM-146)

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