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

Alexander G. Rasin, Jeremy Schiff

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

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).

Original languageEnglish
Pages (from-to)555-568
Number of pages14
JournalJournal of Nonlinear Mathematical Physics
Volume26
Issue number4
DOIs
StatePublished - 2 Oct 2019

Bibliographical note

Publisher Copyright:
© 2019, © 2019 The Authors.

Keywords

  • Bäcklund transformation
  • Hirota-Satsuma
  • Integrable equation
  • Novikov
  • Sawada-Kotera

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