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Galilean symmetry of the KdV hierarchy

Jianghao Xu, Di Yang

Abstract

By solving the infinitesimal Galilean symmetry for the KdV hierarchy, we obtain an explicit expression for the corresponding one-parameter Lie group, which we call the Galilean symmetry of the KdV hierarchy. As an application, we establish an explicit relationship between the non-abelian Born--Infeld partition function and the generalized Brézin--Gross--Witten partition function.

Galilean symmetry of the KdV hierarchy

Abstract

By solving the infinitesimal Galilean symmetry for the KdV hierarchy, we obtain an explicit expression for the corresponding one-parameter Lie group, which we call the Galilean symmetry of the KdV hierarchy. As an application, we establish an explicit relationship between the non-abelian Born--Infeld partition function and the generalized Brézin--Gross--Witten partition function.
Paper Structure (5 sections, 17 theorems, 135 equations)

This paper contains 5 sections, 17 theorems, 135 equations.

Table of Contents

  1. Introduction and statements of the main results
  2. The Galilean symmetry of the KdV hierarchy
  3. The NBI partition function
  4. Application
  5. Generalizations

Key Result

Proposition 1

For any given power series $u({\bf t};\epsilon)\in\mathbb{C}[[{\bf t},\epsilon]]$, the initial value problem has a unique solution $\tilde{u}({\bf t};\epsilon;q)$ in $\mathbb{C}[[{\bf t},\epsilon,q]]$, which has the explicit expression

Theorems & Definitions (34)

  • Proposition 1
  • Theorem 1
  • Remark 1
  • Theorem 2
  • Remark 2
  • Definition 1
  • Proposition 2
  • Lemma 1
  • Theorem 3
  • proof : Proof of Proposition \ref{['prop-galilean-solution']}
  • ...and 24 more