Date and Time
-
Location
Strickland Hall 310
Organizers
Speaker
Ming Chen (University of Pittsburgh)

The Camassa-Holm-Kadomtsev-Petviashvili equation (CH-KP) is a two dimensional generalization of the Camassa-Holm equation which has been recently derived in the context of shallow water waves and nonlinear elasticity. In this talk we will discuss the stability of the one-dimensional traveling waves, solitary or periodic, with respect to two dimensional perturbations which are periodic in the transverse direction. We show that the stability or instability depends on a sign parameter of the transverse dispersion term. In particular, a nonlinear instability of the one-dimensional solitary waves of any size can be proved for the so-called CH-KP-I model, while for one-dimensional periodic waves we are able to obtain spectral instability for small amplitude CH-KP-I waves.  This is a joint work with Lili Fan, Jie Jin, Xingchang Wang and Runzhang Xu.