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SUMMARY:Dmitry Zakharov
DTSTART:20211020T120000Z
DTEND:20211020T130000Z
DTSTAMP:20260423T005811Z
UID:mmandim/27
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/27/"
 >Lumps and lump chain solutions of the KP-I equation</a>\nby Dmitry Zakhar
 ov as part of Mathematical models and integration methods\n\n\nAbstract\nT
 he Kadomstev—Petviashvili equation is one of the fundamental equations i
 n the theory of integrable systems. The KP equation comes in two physicall
 y 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 K
 P-II equation does not have any spatially localized solutions\, but has a 
 rich family of line soliton solutions.\n\nI will discuss two new families 
 of solutions of the KP-I equation\, obtained using the Grammian form of th
 e 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 s
 oliton of KP-II. More generally\, lump chains can form evolving polygonal 
 arrangements whose structure closely resembles that of the line soliton so
 lutions of KP-II. I will also show how lump chains and line solitons may a
 bsorb\, emit\, and reabsorb individual lumps.\n
LOCATION:https://researchseminars.org/talk/mmandim/27/
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