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SUMMARY:Description of the transient processes in waveguides with the mult
 i-contour saddle point method - Kseniia  Kniazeva (Moscow State University
 )
DTSTART:20240702T094500Z
DTEND:20240702T101500Z
UID:TALK215434@talks.cam.ac.uk
DESCRIPTION:A.V. Shanin\, A.I. Korolkov\, K.S. Kniazeva\nA problem of tran
 sient processes description in a waveguide is considered. The waveguide is
  supposed to be closed and homogeneous in the longitudinal direction x.\nT
 he standard approach to this problem is to represent the field as a double
  Fourier integral over frequencies &omega\; and wave numbers k and apply t
 he residue theorem to obtain the field representation in the form of a sum
  of integrals. We propose to transform the letter representation into the 
 integral over some contour on a complex manifold\, which is embedded into 
 the space of two complex variables &omega\; and k. The manifold is the ana
 lytical continuation of the waveguide dispersion diagram.\nWe find asympto
 tical estimation of the integral for large x and fixed x/t (t is time). Fo
 r this purpose\, we build a modification of the saddle point method. The m
 odified saddle point method\, or a multi-contour method\, implies deformat
 ion of the integration contour on the manifold. In case the complex manifo
 ld is too complex\, the contour deformation is difficult. Instead we propo
 se to consider a set of the problems depending parametrically on real x/t\
 , find a set of saddle points for all the problems\, and classify the sadd
 le points on contributing (active) and not contributing (not active) to th
 e field. Following this plan\, one obtains continuous branches of active s
 addle points on the analytically continued dispersion diagram\, these bran
 ches form pulses\, whose contribution to the field can be significant.\nTh
 e set of the saddle points for all real x/t is called a carcass of the dis
 persion diagram. Active carcass branches complement the usual dispersion d
 iagram with real &omega\; and k to form a set of points (&omega\;\, k) cor
 responding to the waves\, which can propagate in the waveguide. We claim t
 hat waveguides can be classified by the type of their carcass.\nHere we sh
 ow this technique for a number of model waveguides.
LOCATION:Seminar Room 1\, Newton Institute
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