Affordable Access

Darboux transformations for two dimensional elliptic affine Toda equations

Authors
  • Zhou, Zi-Xiang
Type
Preprint
Publication Date
Nov 08, 2009
Submission Date
Nov 08, 2009
Identifiers
arXiv ID: 0911.1573
Source
arXiv
License
Yellow
External links

Abstract

The Darboux transformations for the two dimensional elliptic affine Toda equations corresponding to all seven infinite series of affine Kac-Moody algebras, including $A_l^{(1)}$, $A_{2l}^{(2)}$, $A_{2l-1}^{(2)}$, $B_l^{(1)}$, $C_l^{(1)}$, $D_l^{(1)}$ and $D_{l+1}^{(2)}$, are presented. The Darboux transformation is constructed uniformly for the latter six series of equations with suitable choice of spectral parameters and the solutions of the Lax pairs so that all the reality symmetry, cyclic symmetry and complex orthogonal symmetry of the corresponding Lax pairs are kept invariant. The exact solutions of all these two dimensional elliptic affine Toda equations are obtained by using Darboux transformations.

Report this publication

Statistics

Seen <100 times