Canonically Conjugate Variables for the Korteweg-de Vries Equation and the Toda Lattice with Periodic Boundary Conditions

概要

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A new set of canonically conjugate variables is introduced for the periodic Korteweg-de Vries equation and the periodic Toda lattice. These variables are used for reducing both equations to a nonlinear system which can be integrated in terms of theta functions. It becomes clear that the discrete and the continuous problems are, in a sense, isomorphic. Action variables are defined by loop integrals, and the basic oscillation frequencies are computed. In the infinite-period limit, these action variables tend to the ones used in the canonical description of the inverse-scattering solution method.
理論物理学刊行会の論文
1976-02-25