Speaker: Ming Chen, University of Minnesota

Title: Kadomtsev-Petviashvili (KP) equation in a rotating frame

Abstract: The rotation-modied Kadomtsev-Petviashvili (RMKP) equation 
describes small-amplitude, long internal waves propagating in one primary 
direction in a rotating frame of reference. The sign of the dispersion 
parameter makes a big difference in studying the RMKP equation. We show 
that with negative dispersion the Cauchy problem is globally wellposed, 
whereas when considering the solitary waves, only positive dispersion 
allows nontrivial solutions. In the case of weak rotation, we prove the 
ground states of the RMKP are nonlinearly stable. When the rotation 
parameter goes to zero, the corresponding solitary waves approaches to the 
solitary wave of the standard KP equation. This is a joint work with Vera 
Hur and Yue Liu.