A simple-looking relative of the Novikov, Hirota-Satsuma and Sawada-Kotera equations

Abstract

We study the simple-looking scalar integrable equation $f_{xxt}-3(f_x{f}_t-1)=0$, 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).

14 pages, 3 figures