A Hamiltonian equation produces a variety of Painlevé integrable equations: solutions of distinct physical structures
Abdul‐Majid Wazwaz
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.