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

Alexander G. Rasin; Jeremy Schiff

doi:10.1080/14029251.2019.1640465

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

Alexander G. Rasin, Jeremy Schiff

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

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).

Original language	English
Pages (from-to)	555-568
Number of pages	14
Journal	Journal of Nonlinear Mathematical Physics
Volume	26
Issue number	4
DOIs	https://doi.org/10.1080/14029251.2019.1640465
State	Published - 2 Oct 2019

Keywords

Bäcklund transformation
Hirota-Satsuma
Integrable equation
Novikov
Sawada-Kotera

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10.1080/14029251.2019.1640465

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

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 B{\"a}cklund 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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N2 - 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).

AB - 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).

KW - Bäcklund transformation

KW - Hirota-Satsuma

KW - Integrable equation

KW - Novikov

KW - Sawada-Kotera

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

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Keywords

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