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DTSTART:19700329T010000
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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Rational solutions of three integrable equations a
nd applications to rogue waves - Peter Clarkson (U
niversity of Kent)
DTSTART;TZID=Europe/London:20191031T090000
DTEND;TZID=Europe/London:20191031T100000
UID:TALK133492AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/133492
DESCRIPTION:In this talk I shall discuss rational solutions of
the Boussinesq equation\, the focusing nonlinear
Schr"odinger (NLS) equation and the Kadomtsev-Petv
iashvili I (KPI) equation\, which are all soliton
equations solvable by the inverse scattering.

<
br>The Boussinesq equation was introduced by Bouss
inesq in 1871 to describe the propagation of long
waves in shallow water. Rational solutions of the
Boussinesq equation\, which are algebraically deca
ying and depend on two arbitrary parameters\, are
expressed in terms of special polynomials that are
derived through a bilinear equation\, have a simi
lar appearance to rogue-wave solutions of the focu
sing NLS equation and have an interesting structur
e. Conservation laws and integral relations associ
ated with rational solutions of the Boussinesq equ
ation will also be discussed.

Rational sol
utions of the KPI equation will be derived in thre
e ways: from rational solutions of the NLS equatio
n\; from rational solutions of the Boussinesq equa
tion\; and from the spectral problem for the KPI e
quation. It'\;ll be shown that these three fami
lies of rational solutions are fundamentally diffe
rent.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:INI IT
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