Integrability of linear structure of components of modified Korteweg–De Vries hierarchy: multiple soliton solutions and breathers solutions

Abstract

Purpose The purpose of this study is to form a linear structure of components of the modified Korteweg–De Vries (mKdV) hierarchy. The new model includes 3rd order standard mKdV equation, 5th order and 7th order mKdV equations. Design/methodology/approach The authors investigate Painlevé integrability of the constructed linear structure. Findings The Painlevé analysis demonstrates that established sum of integrable models retains the integrability of each component. Research limitations/implications The research also presents a set of rational schemes of trigonometric and hyperbolic functions to derive breather solutions. Practical implications The authors also furnish a variety of solitonic solutions and complex solutions as well. Social implications The work formally furnishes algorithms for extending integrable equations that consist of components of a hierarchy. Originality/value The paper presents an original work for developing Painlevé integrable model via using components of a hierarchy.