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| Ultra-short Pulses |
The cubic nonlinear Schrödinger equation (NLSE) is
the standard approximation for nonlinear Maxwell's equations in optics.
Its derivation assumes a slowly varying amplitude approximation. For
ultra-short pulses, when the width of the pulse is only a few cycles,
this approximation breaks down. In the recent years, together with Gene
Wayne (Boston) , Yeojin Chung (Los Alamos), and Chris Jones (North
Carolina), I have investigated other possible approximations to
nonlinear Maxwell' s equations in the regime of ultra-short pulses. In
2004, Gene and I derived a new equation, the so-called short-pulse
equation (SPE) and we were able to show that the SPE is an excellent
approximation to Maxwell's equations for ultra-short pulses. Many
questions, though, remain open as
- Integrability of the SPE (there is a claim that the
SPE is strongly related to the Sine-Gordon equation)
- Regularization of the SPE using nonlocal terms and
nonlocal solitons
- Extension of the SPE to more complicated geometries
and media
Read more (selected publications):
Y. Chung, C. K. R. T. Jones, T.Schäfer, C.
E. Wayne: Ultra-short pulses in
linear and nonlinear media, Nonlinearity 18
(2005) 1351-1374.
T. Schäfer and C. E. Wayne: Propagation of
ultra-short optical pulses in nonlinear media, Physica D 196 (2004)
90-105.
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