Nonlinear Pulse Propagation
Journées équations aux dérivées partielles (2001), article no. 11, 11 p.

This talk gives a brief review of some recent progress in the asymptotic analysis of short pulse solutions of nonlinear hyperbolic partial differential equations. This includes descriptions on the scales of geometric optics and diffractive geometric optics, and also studies of special situations where pulses passing through focal points can be analysed.

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     title = {Nonlinear {Pulse} {Propagation}},
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     publisher = {Universit\'e de Nantes},
     year = {2001},
     doi = {10.5802/jedp.595},
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     url = {https://proceedings.centre-mersenne.org/articles/10.5802/jedp.595/}
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Jeffrey Rauch. Nonlinear Pulse Propagation. Journées équations aux dérivées partielles (2001), article  no. 11, 11 p. doi : 10.5802/jedp.595. https://proceedings.centre-mersenne.org/articles/10.5802/jedp.595/

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[AR1] D. Alterman and J. Rauch, Diffractive short pulse asymptotics for nonlinear wave equations, Phys. Lett. A. 264(5) 2000, pp. 390-395. | MR | Zbl

[AR2] D. Alterman and J. Rauch, Nonlinear geometric optics for short pulses, Journal of Differential Equations, to appear. | MR | Zbl

[AR3] D. Alterman and J. Rauch, The linear diffractive pulse equation, Methods and Applications of Analysis 7(2001), to appear. | MR | Zbl

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[CR1] R. Carles and J. Rauch, Focusing of spherical nonlinear pulses in ℝ 1+3 , Proc. AMS (2001), to appear | Zbl

[CR2] R. Carles and J. Rauch, Absorption d’impulsions non-linéaires radiales focalisantes dans ℝ 1+3 , Note CRAS, to appear. | MR | Zbl

[CR3] R. Carles and J. Rauch, Diffusion d’impulsions non-linéaires radiales focalisantes dans ℝ 1+3 , Note CRAS to appear. | MR | Zbl

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