A generating function proof of the commutativity of certain Hamiltonian isospectral flows. (English) Zbl 0676.58048
Summary: In a paper by the authors and E. Previato [Commun. Math. Phys. 117, No.3, 451-500 (1988; Zbl 0659.58022)], a ring of Poisson commuting functions which produce isospectral Hamiltonian flows on a space of matrices was described and these flows were related to solutions of associated nonlinear partial differential equations (e.g., the Korteweg- de Vries, nonlinear Schrödinger, and Boussinesq equations). In this letter, we give an alternate proof of the Poisson commutativity of this ring of functions by means of a generating function argument.
MSC:
| 37C10 | Dynamics induced by flows and semiflows |
| 37J40 | Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol’d diffusion |
| 35Q99 | Partial differential equations of mathematical physics and other areas of application |
Keywords:
Hamiltonian flows; nonlinear partial differential equations; Korteweg-de Vries; nonlinear Schrödinger; Boussinesq equationsCitations:
Zbl 0659.58022References:
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