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SUMMARY:Rational solutions of three integrable equations and applications 
 to rogue waves - Peter Clarkson (University of Kent)
DTSTART:20191031T090000Z
DTEND:20191031T100000Z
UID:TALK133492@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:In this talk I shall discuss rational solutions of the Boussin
 esq equation\, the focusing nonlinear Schr"odinger (NLS) equation and the 
 Kadomtsev-Petviashvili I (KPI) equation\, which are all soliton equations 
 solvable by the inverse scattering.<br><br>The Boussinesq equation was int
 roduced by Boussinesq in 1871 to describe the propagation of long waves in
  shallow water. Rational solutions of the Boussinesq equation\, which are 
 algebraically decaying and depend on two arbitrary parameters\, are expres
 sed in terms of special polynomials that are derived through a bilinear eq
 uation\, have a similar appearance to rogue-wave solutions of the focusing
  NLS equation and have an interesting structure. Conservation laws and int
 egral relations associated with rational solutions of the Boussinesq equat
 ion will also be discussed. <br><br>Rational solutions of the KPI equation
  will be derived in three ways: from rational solutions of the NLS equatio
 n\; from rational solutions of the Boussinesq equation\; and from the spec
 tral problem for the KPI equation. It&#39\;ll be shown that these three fa
 milies of rational solutions are fundamentally different.
LOCATION:Seminar Room 1\, Newton Institute
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