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SUMMARY:Two-component Camassa-Holm system and its reductions - Yoshimasa M
 atsuno (Yamaguchi University)
DTSTART:20170809T103000Z
DTEND:20170809T113000Z
UID:TALK75131@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:My talk is mainly concerned with an integrable two-component C
 amassa-Holm (CH2) system which describes the propagation of nonlinear shal
 low water waves. &nbsp\;After a brief review of strongly nonlinear models 
 for shallow water waves including the Green-Naghdi and related systems\, I
  develop a systematic procedure for constructing soliton solutions of the 
 CH2 system.&nbsp\; Specifically\, using a direct method combined with a re
 ciprocal transformation\, I obtain the parametric representation of the mu
 ltisoliton solutions\, and investigate their properties. Subsequently\, I 
 show that the CH2&nbsp\; system reduces to the CH equation and the two-com
 ponent Hunter-Saxton (HS2) system by means of appropriate limiting procedu
 res. The corresponding expressions of the multisoliton solutions are prese
 nted in parametric forms\, reproducing the existing results for the reduce
 d equations. Also\, I discuss the reduction from the HS2 system to the HS 
 equation. Last\, I comment on an interesting issue associated with peaked 
 wave (or peakon) solutions of the CH\, Degasperis-Procesi\, Novikov and mo
 dified CH equations.  &nbsp\;
LOCATION:Seminar Room 1\, Newton Institute
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