Geodesic
Hierarchy of symplectic forms for the Schr\"odinger and the Dirac equations on a line
Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics, Tome 77 (1978), pp. 134-147

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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. 
@article{ZNSL_1978_77_a7,
     author = {P. P. Kulish and A. G. Reiman},
     title = {Hierarchy of symplectic forms for the {Schr\"odinger} and the {Dirac} equations on a line},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {134--147},
     publisher = {mathdoc},
     volume = {77},
     year = {1978},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1978_77_a7/}
}
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P. P. Kulish; A. G. Reiman. Hierarchy of symplectic forms for the Schr\"odinger and the Dirac equations on a line. Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics, Tome 77 (1978), pp. 134-147. http://geodesic.mathdoc.fr/item/ZNSL_1978_77_a7/