2004/10/15 by Adam Doliwa · 2 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Applied mathematics #Bar (unit) #Computer science #Conjugate #Function (biology) #Hierarchy #Integrable system #Interpretation (philosophy) #Law #Mathematical analysis #Mathematics #Nonlinear Waves and Solitons #Physics #Pure mathematics #Quantum chaos and dynamical systems #Ramanujan tau function #nlin.SI
paper · pdf · doi:10.2991/jnmp.2005.12.s1.20
8 pages
arxiv created 2004/10/15 · openalex publication_date 2005/01/01 · arxiv updated 2015/06/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study a potential introduced by Darboux to describe conjugate nets, which within the modern theory of integrable systems can be interpreted as a -function. We investigate the potential using the nonlocal -dressing method of Manakov and Zakharov and we show that it can be interpreted as the Fredholm determinant of an integral equation which naturally appears within that approach. Finally we give some arguments extending that interpretation to multicomponent Kadomtsev-Petviashvili hierarchy.