KP solitons, total positivity, and cluster algebras

Details KP solitons, total positivity, and cluster algebras KP solitons, total positivity, and cluster algebras

2011-05-20

arxiv.org/abs/1105.4170v1

Mathematics

Combinatorics

published in Proc. Natl. Acad. Sci. online ahead of print May 11, 2011, doi:10.1073/pnas.1102627108

Scientific paper

Soliton solutions of the KP equation have been studied since 1970, when Kadomtsev and Petviashvili proposed a two-dimensional nonlinear dispersive wave equation now known as the KP equation. It is well-known that the Wronskian approach to the KP equation provides a method to construct soliton solutions. The regular soliton solutions that one obtains in this way come from points of the totally non-negative part of the Grassmannian. In this paper we explain how the theory of total positivity and cluster algebras provides a framework for understanding these soliton solutions to the KP equation. We then use this framework to give an explicit construction of certain soliton contour graphs, and solve the inverse problem for soliton solutions coming from the totally positive part of the Grassmannian.

Affiliated with

Also associated with

No associations

Rating

KP solitons, total positivity, and cluster algebras does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with KP solitons, total positivity, and cluster algebras, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and KP solitons, total positivity, and cluster algebras will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-712866