skip to content
 

Two-component Camassa-Holm system and its reductions

Presented by: 
Yoshimasa Matsuno Yamaguchi University
Date: 
Wednesday 9th August 2017 - 11:30 to 12:30
Venue: 
INI Seminar Room 1
Abstract: 
My talk is mainly concerned with an integrable two-component Camassa-Holm (CH2) system which describes the propagation of nonlinear shallow water waves.  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.  Specifically, using a direct method combined with a reciprocal transformation, I obtain the parametric representation of the multisoliton solutions, and investigate their properties. Subsequently, I show that the CH2  system reduces to the CH equation and the two-component Hunter-Saxton (HS2) system by means of appropriate limiting procedures. The corresponding expressions of the multisoliton solutions are presented in parametric forms, reproducing the existing results for the reduced 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 modified CH equations.  
The video for this talk should appear here if JavaScript is enabled.
If it doesn't, something may have gone wrong with our embedded player.
We'll get it fixed as soon as possible.
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons