Geometry of Integrable Systems Related to the Restricted Grassmannian
Tomasz Goli\'nski, Alice Barbara Tumpach
TL;DR
This paper explores the geometric structure of integrable systems connected to the restricted Grassmannian, focusing on differential equations, flows, and momentum maps within a Banach Lie-Poisson framework.
Contribution
It introduces a new geometric perspective on integrable systems related to the restricted Grassmannian, including the analysis of flows and momentum maps.
Findings
Describes flows on the groupoid of partial isometries and on the restricted Grassmannian.
Establishes a momentum map framework for these integrable systems.
Provides insights into the geometric structure underlying these differential equations.
Abstract
A hierarchy of differential equations on a Banach Lie-Poisson space related to the restricted Grassmannian is studied. Flows on the groupoid of partial isometries and on the restricted Grassmannian are described, and a momentum map picture is presented.
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Taxonomy
TopicsNonlinear Waves and Solitons · Advanced Differential Equations and Dynamical Systems · Advanced Algebra and Geometry