| 概要 | In this talk I propose and analyze a generalized two-component Camassa-Holm system which can be derived
from the theory of shallow water waves moving over a linear shear flow.
This new system also generalizes a class of dispersive waves in cylindrical compressible hyperelastic rods.
I will show in the first part of the talk
that this new system can still exhibit the wave-breaking phenomenon.
I also establish a sufficient condition for global solutions. In the second part of the talk,
I will study the solitary wave solutions of the generalized two-component Camassa-Holm system.
In addition to those smooth solitary-wave solutions,
I will show that there are solitary waves with singularities:
peaked and cusped solitary waves. I also demonstrate that all smooth solitary waves
are orbitally stable in the energy space. |