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Darboux Transformations for a Lax Integrable System in 2n Dimensions

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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.

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Authors and Affiliations

  1. Institute of Mathematics, Automath Institut, Fudan University, Universität-GH Paderborn, Shanghai, Paderborn, 200433, D-33098, P.R., China, Germany

    Wen-Mu Ma

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  1. Wen-Mu Ma
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Correspondence to Wen-Mu Ma.

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Mathematics Subject Classifications (1991): 58F07, 35Q58, 58G35.

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Ma, WM. Darboux Transformations for a Lax Integrable System in 2n Dimensions. Lett Math Phys 39, 33–49 (1997). https://doi.org/10.1007/s11005-997-3049-3

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  • DOI: https://doi.org/10.1007/s11005-997-3049-3

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