Darboux Transformations for a Lax Integrable System in $2n$-Dimensions

Abstract

A $2n$-dimensional Lax integrable system is proposed by a set of specific spectral problems. It contains Takasaki equations, the self-dual Yang-Mills equations and its integrable hierarchy as examples. An explicit formulation of Darboux transformations is established for this Lax integrable system. The Vandermonde and generalized Cauchy determinant formulas lead to a description for deriving explicit solutions and thus some rational and analytic solutions are obtained.

Latex, 14 pages, to be published in Lett. Math. Phys

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