Alterman, Deborah; Rauch, Jeffrey Diffractive short pulse asymptotics for nonlinear wave equations. (English) Zbl 0947.35033 Phys. Lett., A 264, No. 5, 390-395 (2000). Summary: We present an algorithm for constructing approximate solutions to nonlinear wave propagation problems in which diffractive effects and nonlinear effects come into play on the same time scale. The approximate solutions describe the propagation of short pulses. In a separate paper the equations used to construct the approximate solutions are derived using the method of multiple scales and the approximate solutions are proved accurate in the short wavelength limit. We present numerical studies which even in the linear case indicate significant qualitative differences between these approximations and those derived using the slowly varying envelope ansatz. Cited in 1 ReviewCited in 13 Documents MSC: 35C20 Asymptotic expansions of solutions to PDEs 78A60 Lasers, masers, optical bistability, nonlinear optics 35L70 Second-order nonlinear hyperbolic equations Keywords:method of multiple scales; short wavelength limit; slowly varying envelope ansatz PDFBibTeX XMLCite \textit{D. Alterman} and \textit{J. Rauch}, Phys. Lett., A 264, No. 5, 390--395 (2000; Zbl 0947.35033) Full Text: DOI References: [1] Hänsch, T. W., Opt. Commun., 80, 71 (1990) [2] Ziolkowski, R. W., Phys. Rev. A, 39, 2005 (1989) [3] Hellwarth, R. W.; Nouchi, P., Phys. Rev. E, 54, 889 (1996) [4] Hile, C., Wave Motion, 24, 1 (1996) [5] Hile, C. V.; Kath, W. L., J. Opt. Soc. Am. B, 13, 1135 (1996) [6] Feng, S.; Winful, H. G.; Hellwarth, R. W., Phys. Rev. E, 59, 4630 (1999) [7] Rothenberg, J. E., Opt. Lett., 17, 1340 (1992) [8] Esarey, E.; Sprangle, P.; Pilloff, M.; Krall, J., J. Opt. Soc. Am. B, 12, 1695 (1995) [9] Brabec, T.; Krausz, F., Phys. Rev. Letters, 78, 3282 (1997) [10] Porras, M. A., Phys. Rev. E, 58, 1086 (1998) [11] Kaplan, A. E., J. Opt. Soc. Am. B, 15, 951 (1998) [12] Ranka, J. K.; Gaeta, A. L., Opt. Lett., 23, 534 (1998) [13] D. Alterman, Diffractive Nonlinear Geometric Optics for Short Pulses, Ph.D. thesis, University of Michigan, (1999).; D. Alterman, Diffractive Nonlinear Geometric Optics for Short Pulses, Ph.D. thesis, University of Michigan, (1999). · Zbl 1036.35049 [14] D. Alterman, J. Rauch, Diffractive Nonlinear Geometric Optics for Short Pulses, in preparation.; D. Alterman, J. Rauch, Diffractive Nonlinear Geometric Optics for Short Pulses, in preparation. · Zbl 1036.35049 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.