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SUMMARY:Reductions of  (2+1) and (3+1) Dimensional Kadomtsev- Petviashvili
  Type Equations and Dispersive Shock Waves - Ali Demirci (Instanbul Techni
 cal University)
DTSTART:20220714T100000Z
DTEND:20220714T103000Z
UID:TALK175877@talks.cam.ac.uk
DESCRIPTION:In our recent works\, dispersive shock waves (DSWs) in the (2+
 1) and (3+1) dimensional Kadomtsev- Petviashvili type equations (KP\, modi
 fied KP and Gardner-KP equations) were studied with a step-like initial co
 ndition along some chosen special fronts. By using a similarity reduction\
 , the problem of studying DSWs in the multidimensional equations reduced t
 o finding DSW solution of a (1+1) dimensional equations. Whitham modulatio
 n equations were derived which describes DSW evolution in the reduced equa
 tions by using the method of multiple scales. These equations were written
  in terms of appropriate Riemann type variables to obtain the Whitham syst
 ems of the reduceded (1+1) dimensional equations. DSW solutions which were
  obtained from the numerical solutions of the Whitham systems and the dire
 ct numerical solution of the reduced (1+1) dimensional equations were comp
 ared. In this comparison\, an agreement was found between these solutions.
  Also\, some physical qualitative results about DSWs in the reduced equati
 ons were presented. DSW solutions in the reduced equations provide some in
 formation about DSW behavior along the intial fronts in the reduced equati
 ons. In this talk\, I will compare the similarities and distinctions of DS
 W solutions of these reduced (1+1) dimensional equations. I will also disc
 uss how DSW solutions of these reduced equations can be used to construct 
 DSW solutions of the original mutidimensional equations.
LOCATION:Seminar Room 1\, Newton Institute
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