https://doi.org/10.1140/epjp/s13360-025-06670-w
Regular Article
Pfaffian solutions to the Hirota–Satsuma–Ito equation
Physics Department, Mimar Sinan Fine Arts University, Bomonti, 34380, Istanbul, Turkey
Received:
28
March
2025
Accepted:
17
July
2025
Published online:
8
August
2025
This paper investigates the (2+1)-dimensional Hirota–Satsuma–Ito (HSI) equation. We derive explicit soliton solutions up to three-solitons using the Hirota direct method. The Pfaffian formulation of the equation is the essential part of the study. We give Pfaffian formulation of the HSI equation and use it to prove the 
soliton generalization of the solutions. Furthermore, we present and analyze various particular solutions derived from the Pfaffian formulation, including solitons, breathers, kink-type solitons and breathers, and their interactions.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
