This article is cited in 3 papers

Nonlocal symmetries of some nonlinear partial differential equations with third-order Lax pairs

Xiazhi Hao

College of Science, Zhejiang University of Technology, Hangzhou, China

Abstract: By including spectral functions, we obtain nonlocal symmetries equivalent to Lie point symmetries of the corresponding extended systems for the Boussinesq equation, the modified generalized Vakhnenko equation, the Hirota–Satsuma equation, and the Sawada–Kotera equation. All considered equations have third-order Lax pairs, which allows studying their nonlocal symmetries in a unified way.

Keywords: nonlocal symmetry, Boussinesq equation, modified generalized Vakhnenko equation, Hirota–Satsuma equation, Sawada–Kotera equation.

MSC: 34M45;76M60

Received: 12.10.2020
Revised: 12.10.2020

DOI: 10.4213/tmf9997

 English version: Theoretical and Mathematical Physics, 2021, 206:2, 119–127

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