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arXiv · 2503.05635

Method of ${\cal M}_{n}$-Extension via Frobenius Companion Matrices

Metin Gürses·Aslı Pekcan
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Abstract

Frobenius companion matrices arise when we write an $n$-th order linear ordinary differential equation as a system of first order differential equations. These matrices and their transpose have very nice properties. By using the powers of these matrices we form a closed algebra under the matrix multiplication. Structure constants of this commuting algebra are the components of companion matrix. We use these matrices in our method of ${\cal M}_{n}$-extension of scalar integrable equations to produce new systems of integrable equations with recursion operators.

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Metin Gürses, Aslı Pekcan. 2025-03-07. Method of ${\cal M}_{n}$-Extension via Frobenius Companion Matrices. https://arxiv.org/abs/2503.05635

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