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SUMMARY:Asymptotic soliton-like solutions to the Korteweg-de Vries equatio
n with variable coefficients and singular perturbation
DTSTART;VALUE=DATE-TIME:20220517T131500Z
DTEND;VALUE=DATE-TIME:20220517T141500Z
DTSTAMP;VALUE=DATE-TIME:20220810T071222Z
UID:indico-event-7906@indico.math.cnrs.fr
DESCRIPTION:The talk deals with the Korteweg-de Vries equation with variab
le coefficients and a small parameter at the highest derivative. These pro
blems arise while studying wave processes in media with variable character
istics and a small dispersion.\n\nAn approach to the construction of asymp
totic soliton-like solution of the equation is presented. The approach is
based on the non-linear WKB technique. The algorithm for constructing the
asymptotic soliton-like solution is described in detail\, as well as its j
ustification.\n\nThe constructed asymptotic solution is similar to the sol
iton solution of the Korteweg-de Vries equation $ u_t+uu_x+u_{xxx}=0 $. Th
e solution contains regular and singular parts of asymptotic. The regular
part of the solution forms the background of the wave process\, and its si
ngular part reflects the features associated with the specific properties
of the soliton. Differential equations for the terms of the asymptotics ar
e given and their solving is discussed.\n\nThe problem of the existence of
a global asymptotic soliton-like solution of the equation is also conside
red.\n\nThe obtained results are illustrated by examples.\n\nhttps://indic
o.math.cnrs.fr/event/7906/
LOCATION:ICJ Fokko
URL:https://indico.math.cnrs.fr/event/7906/
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