Painleve analysis, Backlund transformation, Lax pair and periodic wave solutions for a generalized (2+1)-dimensional Hirota-Satsuma-Ito equation in fluid mechanics

TL;DR

This paper analyzes a generalized (2+1)-dimensional Hirota-Satsuma-Ito equation in fluid mechanics, establishing its integrability, constructing transformations and Lax pairs, and deriving periodic wave solutions.

Contribution

It introduces a new integrability analysis, bilinear forms, Backlund transformation, and periodic solutions for the generalized Hirota-Satsuma-Ito equation.

Findings

The equation is Painleve integrable under certain conditions.

Constructed bilinear form, Backlund transformation, and Lax pair.

Derived and visualized periodic wave solutions.

Abstract

In this paper, we investigate a generalized (2+1)-dimensional Hirota-Satsuma-Ito (HSI) equation in fluid mechanics. Via the Painleve analysis, we find that the HSI equation is Painleve integrable under certain condition. Bilinear form, Bell-polynomial-type Backlund transformation and Lax pair are constructed with the binary Bell polynomials. One periodic-wave solutions are derived via the Hirota-Riemann method and displayed graphically.