Dynamics of Partial Differential Equations

Volume 6 (2009)

Number 4

Wave breaking in the short-pulse equation

Pages: 291 – 310

DOI: https://dx.doi.org/10.4310/DPDE.2009.v6.n4.a1

Authors

Yue Liu (Department of Mathematics, University of Texas at Arlington)

Dmitry Pelinovsky (Department of Mathematics, McMaster University, Hamilton, Ontario, Canada)

Anton Sakovich (Department of Mathematics, McMaster University, Hamilton, Ontario, Canada)

Abstract

Sufficient conditions for wave breaking are found for the shortpulse equation describing wave packets of few cycles on the ultra-short pulse scale. The analysis relies on the method of characteristics and conserved quantities of the short-pulse equation and holds both on an infinite line and in a periodic domain. Numerical illustrations of the finite-time wave breaking are given in a periodic domain.

Keywords

wave breaking, ultra-short pulse, short-pulse equation

2010 Mathematics Subject Classification

35-xx, 76-xx

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Published 1 January 2009