Abstract
The formalism of classical r-matrices is used to construct families of compatible Poisson brackets for some nonlinear integrable systems connected with Virasoro algebras. We recover the coupled KdV [1] and Harry Dym [2] systems associated with the auxiliary linear problem
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Fordy, A.P., Reyman, A.G. & Semenov-Tian-Shansky, M.A. Classical r-matrices and compatible Poisson brackets for coupled KdV systems. Lett Math Phys 17, 25–29 (1989). https://doi.org/10.1007/BF00420010
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DOI: https://doi.org/10.1007/BF00420010