Geometrization of the Lax Pair Tensors
D. Baleanu, S. Baskal
TL;DR
This paper presents a geometric tensorial formulation of Lax pair equations incorporating Cartan's torsion, analyzes 3D spacetimes with Lax tensors, and explores solutions like separable coordinates and the Toda lattice.
Contribution
It introduces a new geometric tensorial framework for Lax pairs, including torsion, and provides detailed analysis of 3D spacetime solutions and their applications.
Findings
Tensorial form of Lax equations with torsion
Analysis of 3D spacetimes with Lax tensors
Examples including separable coordinates and Toda lattice
Abstract
The tensorial form of the Lax pair equations are given in a compact and geometrically transparent form in the presence of Cartan's torsion tensor. Three-dimensional spacetimes admitting Lax tensors are analyzed in detail. Solutions to Lax tensor equations include interesting examples as separable coordinates and the Toda lattice.
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