Inverse Scattering Technique of Soliton Theory, Lie Algebras, the Quantum Mechanical Poisson-Moyal Bracket, and the Rotating Rigid Body

Robert Hermann

doi:10.1103/PhysRevLett.37.1591

Inverse Scattering Technique of Soliton Theory, Lie Algebras, the Quantum Mechanical Poisson-Moyal Bracket, and the Rotating Rigid Body

Robert Hermann

Phys. Rev. Lett. 37, 1591 – Published 13 December 1976

Abstract

The Lax equation of nonlinear wave theory is described in a purely Lie-algebraic context. A realization—independent of linear operator theory—which leads to the Kortewegde Vries equation is described in terms of the Poisson-Moyal Lie algebra of quantum mechanics. This approach leads to a generalization of the Euler rigid-body equations.

Received 2 September 1976

DOI:https://doi.org/10.1103/PhysRevLett.37.1591

Authors & Affiliations

Robert Hermann^*

Department of Physics, Harvard University, Cambridge, Massachusetts 02131

^*On leave from Rutgers University. National Research Council Senior Research Associate at NASA-Ames Laboratory. Also supported in part by National Science Foundation under Grants No. MPS75-20427 and No. 07993.