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On the Korteweg–de Vries equation: Frequencies and initial value problem
The Korteweg-de Vries equation (KdV)is a completely integrable system with phase space L 2 (S 1 ).Although the Hamiltonian H(qis defined only on the dense subspace H 1 (S 1 ), we prove that the frequencies ω j = ∂H ∂Jj can be defined on the whole space L 2 …