A simple-looking relative of the Novikov, Hirota-Satsuma and Sawada-Kotera equations. Issue 4 (2nd October 2019)

• Record Type: Journal Article
• Authors: Rasin, Alexander G.; Schiff, Jeremy
• Is Part Of: Journal of nonlinear mathematical physics. Volume 26:Issue 4(2019)
• Page Start: 555
• Page End: 568
• Publication Date: 2019-10-02
• Subjects: Integrable equation -- Novikov -- Hirota-Satsuma -- Sawada-Kotera -- Bäcklund transformation; 35Q58 -- 37K05 -- 37K10 -- 37K35 -- 37K40 -- 37K45 -- 70G65; Nonlinear theories -- Periodicals; Mathematical physics -- Periodicals; 515.252
• DOI: 10.1080/14029251.2019.1640465
• Languages: English
• ISSNs: 1402-9251

Abstract

Abstract : We study the simple-looking scalar integrable equation fxxt 3( fx ft 1) = 0, which is related (in different ways) to the Novikov, Hirota-Satsuma and Sawada-Kotera equations. For this equation we present a Lax pair, a Bäcklund transformation, soliton and merging soliton solutions (some exhibiting instabilities), two infinite hierarchies of conservation laws, an infinite hierarchy of continuous symmetries, a Painlevé series, a scaling reduction to a third order ODE and its Painlevé series, and the Hirota form (giving further multisoliton solutions).