演講訊息 TALKS

We study 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. In the first part of the talk, we show that this new system can still exhibit the ave-breaking phenomenon. We also establish a sufficient condition for global solutions. In the second part of the talk, we study the existence of solitary-wave solutions of a generalized two-component Camassa-Holm system. In addition to those smooth solitary-wave solutions, we show that there are solitary waves with singularities: peaked and cusped solitary waves. We also demonstrate that all smooth solitary waves are orbitally stable in the energy space.