A family of integrable evolution equations of third order. Issue 1 (2nd January 2017)

• Record Type: Journal Article
• Authors: Babela, Matthew; Odesskii, Alexandre
• Is Part Of: Journal of nonlinear mathematical physics. Volume 24:Issue 1(2017)
• Page Start: 73
• Page End: 78
• Publication Date: 2017-01-02
• Subjects: Integrable Equations -- Differential substitutions -- Krichever-Novikov equation -- 35Q58 -- 37K05 -- 37K10 -- 37K25; Nonlinear theories -- Periodicals; Mathematical physics -- Periodicals; 515.252
• DOI: 10.1080/14029251.2017.1282244
• Languages: English
• ISSNs: 1402-9251

Abstract

Abstract : We construct a family of integrable equations of the form vt = f ( v ; vx ; vxx ; vxxx ) such that f is a transcendental function in v ; vx ; vxx . This family is related to the Krichever-Novikov equation by a differential substitution. Our construction of integrable equations and the corresponding differential substitutions involves geometry of a family of genus two curves and their Jacobians.