The method of <i>M<sub>n</sub></i>-extension: The KdV equation

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GÜRSES M., PEKCAN YILDIZ A.

PHYSICS LETTERS A, 2025 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Publication Date: 2025
  • Doi Number: 10.1016/j.physleta.2024.130217
  • Journal Name: PHYSICS LETTERS A
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Chemical Abstracts Core, Communication Abstracts, Compendex, INSPEC, Metadex, Philosopher's Index, zbMATH, DIALNET, Civil Engineering Abstracts
  • Hacettepe University Affiliated: Yes

Abstract

In this work we generalize M-2-extension that has been introduced recently. For illustration we use the KdV equation. We present five different M-3-extensions of the KdV equation and their recursion operators. We give a compact form of M-n-extension of the KdV equation and recursion operator of the coupled KdV system. The method of M-n-extension can be applied to any integrable scalar equation to obtain integrable multi-field system of equations. We also present unshifted and shifted nonlocal reductions of an example of M-3-extension of KdV.