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.
@incollection{JEDP_2001____A11_0, author = {Rauch, Jeffrey}, title = {Nonlinear {Pulse} {Propagation}}, booktitle = {}, series = {Journ\'ees \'equations aux d\'eriv\'ees partielles}, eid = {11}, pages = {1--11}, publisher = {Universit\'e de Nantes}, year = {2001}, doi = {10.5802/jedp.595}, mrnumber = {1843412}, zbl = {1021.35062}, language = {en}, url = {http://www.numdam.org/articles/10.5802/jedp.595/} }
Rauch, Jeffrey. Nonlinear Pulse Propagation. Journées équations aux dérivées partielles (2001), article no. 11, 11 p. doi : 10.5802/jedp.595. http://www.numdam.org/articles/10.5802/jedp.595/
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