Speaker : Prof. Yuji Kodama (The Ohio State University, Columbus, USA)
Title : On the stability and soliton resolution for the KP equation
Time : 2018-07-04 (Wed) 14:30 - 15:30
Place : Seminar Room 722, Institute of Mathematics (NTU Campus)
Abstract: In the first part of my talk, I will start to discuss the transversal stability of the KdV soliton in terms of the KP equation. Based on a simple perturbation argument, one can show that an amplitude modulation generates a local phase shift which propagates along the soliton crest. This implies that the soliton is unstable in any norm with the entire $\mathbb{R}^2$. However the phase shift eventually escapes from any compact space in $\mathbb{R}^2$. This result is consistent with the recent result of the stability problem by Mizumachi.

The second part of my talk provides a brief summary of a combinatorial aspect of soliton solutions of the KP equation, the KP solitons. Then I demonstrate numerical results of the KP equation with certain class of initial waves. The goal of this part is to show how one can predict the asymptotic solutions based on the combinatorial properties of the KP solitons. As a specific example, I will discuss the Mach reflection problem which describes a resonant interaction of solitary waves appearing in the reflection of an obliquely incident wave onto a vertical wall.