Classical r-matrices and compatible Poisson brackets for coupled KdV systems
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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 .
$$\sum\limits_{i = 0}^N {\lambda '\left( {a_i \frac{{{\text{d}}^{\text{2}} }}{{{\text{dx}}^2 }} + {\text{u}}_{\text{i}} } \right)} \psi = 0$$
(1)
AMS subject classification (1980)
58F07Preview
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References
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