On Möbius‐invariant and symmetry‐integrable evolution equations and the Schwarzian derivative. Issue 2 (3rd May 2019)

• Record Type: Journal Article
• Authors: Euler, Marianna; Euler, Norbert
• Is Part Of: Studies in applied mathematics. Volume 143:Issue 2(2019)
• Page Start: 139
• Page End: 156
• Publication Date: 2019-05-03
• Subjects: dynamical systems -- mathematical physics -- partial differential equations; Mathematics -- Periodicals; Mathématiques -- Périodiques; Mathématique; Mathématique appliquée; Ressource Internet (Descripteur de forme); Périodique électronique (Descripteur de forme); 519
• DOI: 10.1111/sapm.12268
• Languages: English
• ISSNs: 0022-2526

Abstract

Abstract: We consider symmetry‐integrable evolution equations in 1 + 1 dimensions of order 3 and order 5. We show that there exist only three equations in this class that are invariant under the Möbius transformation, and we name those Schwarzian equations. We report an interesting relation between the recursion operators of the Schwarzian equations and the corresponding adjoint operators that generate hierarchies of Schwarzian systems in terms of the Schwarzian derivative. This indicates a deep relation between the Schwarzian equations and the Schwarzian derivative. A classification of the fully nonlinear third‐order Schwarzian equations is also reported.