Abstract
A sequence of symplectic forms have been constructed, relative to each of which the Korteweg-de Vries equation and all its higher analogs are Hamiltonian. The well-known conservation laws serve as the Hamiltonians. An analogous system of forms has been constructed also for a family of equations solvable by use of the inverse scattering problem for the Dirac operator. The results are used in the investigation of the connection between various non-linear evolution equations.
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Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im, V. A. Steklova AN SSSR, Vol. 77, pp. 134–147, 1978.
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Kulish, P.P., Reiman, A.G. Hierarchy of symplectic forms for the Schrödinger and the Dirac equations on a line. J Math Sci 22, 1627–1637 (1983). https://doi.org/10.1007/BF01375613
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DOI: https://doi.org/10.1007/BF01375613