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تسجيل مستخدم جديدPoisson $lambda$-brackets for differential-difference equations
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We introduce the notion of a multiplicative Poisson $lambda$-bracket, which plays the same role in the theory of Hamiltonian differential-difference equations as the usual Poisson $lambda$-bracket plays in the theory of Hamiltonian PDE. We classify multiplicative Poisson $lambda$-brackets in one difference variable up to order 5. Applying the Lenard-Magri scheme to a compatible pair of multiplicative Poisson $lambda$-brackets of order 1 and 2, we establish integrability of some differential-difference equations, generalizing the Volterra chain.
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