On computation of Darboux polynomials for full Toda lattice
A.V. Tsiganov
TL;DR
This paper demonstrates that combining classical methods with modern symbolic algebra tools and sufficient computing power enables the computation of Darboux invariants for the full Toda lattice, an important integrable system.
Contribution
It shows that Darboux polynomials for the full Toda lattice can be computed without extra information using standard methods and symbolic algebra.
Findings
Successful computation of Darboux invariants for the Toda lattice
Validation of classical methods with modern computational tools
No additional information needed for invariant computation
Abstract
One of the oldest methods for computing invariants of ordinary differential equations is tested using the full Toda lattice model. We show that the standard method of undetermined coefficients and modern symbolic algebra tools together with sufficient computing power allow to compute Darboux invariants without any additional information.
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Taxonomy
TopicsMathematical functions and polynomials · Holomorphic and Operator Theory