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

Abstract

PurposeThe purpose of this paper is to investigate a variety of Painlevé integrable equations derived from a Hamiltonian equation.Design/methodology/approachThe 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.FindingsThe developed Hamiltonian models exhibit complete integrability in analogy with the original equation.Research limitations/implicationsThe 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 implicationsThe work introduces six Painlevé-integrable equations developed from a Hamiltonian model.Social implicationsThe work presents useful algorithms for constructing new integrable equations and for handling these equations.Originality/valueThe paper presents an original work with newly developed integrable equations and shows useful findings.