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A simple-looking relative of the Novikov, Hirota-Satsuma and Sawada-Kotera equations
Journal of Nonlinear Mathematical Physics ( IF 0.7 ) Pub Date : 2019-07-09 , DOI: 10.1080/14029251.2019.1640465
Alexander G. Rasin , Jeremy Schiff

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).

中文翻译:

Novikov、Hirota-Satsuma 和 Sawada-Kotera 方程的一个简单的亲戚

我们研究了看似简单的标量可积方程 fxxt 3( fx ft 1) = 0,它与 Novikov、Hirota-Satsuma 和 Sawada-Kotera 方程相关(以不同方式)。对于这个方程,我们提出了一个 Lax 对、一个 Bäcklund 变换、孤子和合并孤子解(一些表现出不稳定性)、守恒定律的两个无限层次、连续对称的无限层次、Painlevé 级数、到三阶 ODE 的缩放缩减及其 Painlevé 系列,以及 Hirota 形式(提供进一步的多孤子解决方案)。
更新日期:2019-07-09
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