A tensorial Lax pair equation and integrable systems in relativity and classical mechanics

Details A tensorial Lax pair equation and integrable systems in relativity and classical mechanics A tensorial Lax pair equation and integrable systems in relativity and classical mechanics

1994-10-11

arxiv.org/abs/gr-qc/9410011v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

7 pages

Scientific paper

It is shown that the Lax pair equation dL/dt = [L,A] can be given a neat tensorial interpretation for finite-dimensional quadratic Hamiltonians. The Lax matrices L and A are shown to arise from third rank tensors on the configuration space. The second Lax matrix A is related to a connection which characterizes the Hamiltonian system. The Toda lattice system is used to motivate the definition of the Lax pair tensors. The possible existence of solutions to the Einstein equations having the Lax pair property is discussed.

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