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arXiv · 1905.02179

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

Alexander G. Rasin·Jeremy Schiff
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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 B\"acklund transformation, soliton and merging soliton solutions (some exhibiting instabilities), two infinite hierarchies of conservation laws, an infinite hierarchy of continuous symmetries, a Painlev\'e series, a scaling reduction to a third order ODE and its Painlev\'e series, and the Hirota form (giving further multisoliton solutions).

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Alexander G. Rasin, Jeremy Schiff. 2019-05-06. A simple-looking relative of the Novikov, Hirota-Satsuma and Sawada-Kotera equations. https://arxiv.org/abs/1905.02179

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