Pfaffian solutions to the Hirota–Satsuma–Ito equation

Abstract

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 N-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. © The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2025.