Volterra's realization of the KM-system
M. A. Agrotis, P. A. Damianou
TL;DR
This paper constructs a symplectic realization of the KM-system using Volterra's transformation, deriving higher order Poisson tensors and commuting flows, and applying Oevel's theorem to find symmetries and invariants.
Contribution
It introduces a novel symplectic realization of the KM-system by doubling variables and employs recursion operators and Oevel's theorem for advanced structural insights.
Findings
Derived higher order Poisson tensors
Established commuting flows for the KM-system
Identified master symmetries and invariants
Abstract
We construct a symplectic realization of the KM-system and obtain the higher order Poisson tensors and commuting flows via the use of a recursion operator. This is achieved by doubling the number of variables through Volterra's coordinate transformation. An application of Oevel's theorem yields master symmetries, invariants and deformation relations.
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Taxonomy
TopicsNonlinear Waves and Solitons