Date/Time
Date(s) - 04/11/2022
3:30 pm - 4:30 pm

CANCELLED – Rescheduled March 17, 2023


Speaker: Dmitry Zakharov (Central Michigan University) 

Title: Lump chains in the KP-I equation

Abstract: The Kadomstev–Petviashvili equation is one of the fundamental equations in the theory of integrable systems. The KP equation comes in two physically distinct forms: KP-I and KP-II. The KP-I equation has a large family of rational solutions known as lumps. A single lump is a spatially localized soliton, and lumps can scatter on one another or form bound states. The KP-II equation does not have any spatially localized solutions, but has a rich family of line soliton solutions that form evolving polygonal patterns.

I will discuss two new families of solutions of the KP-I equation, obtained using the Grammian form of the tau-function. The first is the family of lump chain solutions. A single lump chain consists of a linear arrangement of lumps, similar to a line soliton of KP-II. More generally, lump chains can form evolving polygonal arrangements whose structure closely resembles that of the line soliton solutions of KP-II. I will also show how lump chains and line solitons may absorb, emit, and reabsorb individual lumps.

Joint work with Andrey Gelash, Charles Lester, Yury Stepanyants, and Vladimir Zakharov.

Location: Hamilton Hall 305

Coffee and Cookies will be served in Hamilton Hall 305 at 3:00 pm. Everyone is welcome.