Infinitesimal Darboux transformation and semi-discrete MKDV equation. (7th April 2022)

• Record Type: Journal Article
• Authors: Cho, Joseph; Rossman, Wayne; Seno, Tomoya
• Is Part Of: Nonlinearity. Volume 35:Number 4(2022)
• Page Start: 2134
• Page End: 2146
• Publication Date: 2022-04-07
• Subjects: infinitesimal Darboux transformation -- semi-discrete mKdV equation -- discrete differential geometry; primary 53A70 -- secondary 35Q53 -- 53A04; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/1361-6544/ac591f
• Languages: English
• ISSNs: 0951-7715

Abstract

Abstract: We connect certain continuous motions of discrete planar curves resulting in semi-discrete potential Korteweg–de Vries (mKdV) equation with Darboux transformations of smooth planar curves. In doing so, we define infinitesimal Darboux transformations that include the aforementioned motions, and also give an alternate geometric interpretation for establishing the semi-discrete potential mKdV equation.