A Hamiltonian equation produces a variety of Painlevé integrable equations: solutions of distinct physical structures

Abstract

Purpose

The purpose of this paper is to investigate a variety of Painlevé integrable equations derived from a Hamiltonian equation.

Design/methodology/approach

The newly developed Painlevé integrable equations have been handled by using Hirota’s direct method. The authors obtain multiple soliton solutions and other kinds of solutions for these six models.

Findings

The developed Hamiltonian models exhibit complete integrability in analogy with the original equation.

Research limitations/implications

The present study is to address these two main motivations: the study of the integrability features and solitons and other useful solutions for the developed equations.

Practical implications

The work introduces six Painlevé-integrable equations developed from a Hamiltonian model.

Social implications

The work presents useful algorithms for constructing new integrable equations and for handling these equations.

Originality/value

The paper presents an original work with newly developed integrable equations and shows useful findings.

Citation

Wazwaz, A.-M. (2024), "A Hamiltonian equation produces a variety of Painlevé integrable equations: solutions of distinct physical structures", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 34 No. 4, pp. 1730-1751. https://doi.org/10.1108/HFF-12-2023-0727