Abstract
AbstractWe 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.
Funder
Japan Society for the Promotion of Science
Subject
Applied Mathematics,General Physics and Astronomy,Mathematical Physics,Statistical and Nonlinear Physics
Reference56 articles.
1. Om ytor med konstant negativ krökning;Bäcklund;Lunds Univ. Årsskrift,1883
2. Non-special, non-canal isothermic Tori with spherical lines of curvature;Bernstein;Trans. Am. Math. Soc.,2001
3. Sulla trasformazione di Bäcklund per le superficie pseudosferiche;Bianchi;Rend. Lincei,1892
4. Ricerche sulle superficie isoterme e sulla deformazione delle quadriche;Bianchi;Ann. Math. Pure Appl.,1904
5. Complementi alle ricerche sulle superficie isoterme;Bianchi;Ann. Math. Pure Appl.,1905
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