Generalized discrete integrable operator and integrable hierarchy

2025/11/07 by Huan Liu, Liu, Huan
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics

paper · pdf · doi:10.48550/arxiv.2511.05046

openalex publication_date 2025/11/07 · openalex created_date 2025/11/11 · openalex updated_date 2026/07/28

Abstract

We introduce and systematically develop two classes of discrete integrable operators: those with 2× 2 matrix kernels and those possessing general differential kernels, thereby generalizing the discrete analogue previously studied. A central finding is their inherent connection to higher-order pole solutions of integrable hierarchies, contrasting sharply with standard operators linked to simple poles. This work not only provides explicit resolvent formulas for matrix kernels and differential operator analogues but also offers discrete integrable structures that encode higher-order behaviour.

Citations

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