2024/07/18 by A. Zotov, Zotov, A. · 2 citations
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.2407.13854
openalex publication_date 2024/07/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Lax pair for the field analogue of the classical spin elliptic Calogero-Moser is proposed. Namely, using the previously known Lax matrix we suggest an ansatz for the accompany matrix. The presented construction is valid when the matrix of spin variables \mathcal S∈\rm Mat(N,\mathbb C) satisfies the condition \mathcal S2=c0\mathcal S with some constant c0∈\mathbb C. It is proved that the Lax pair satisfies the Zakharov-Shabat equation with unwanted term, thus providing equations of motion on the unreduced phase space. The unwanted term vanishes after additional reduction. In the special case \rm rank(\mathcal S)=1 we show that the reduction provides the Lax pair of the spinless field Calogero-Moser model obtained earlier by Akhmetshin, Krichever and Volvovski.