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.
The authors investigate Painlevé integrability of the constructed linear structure.
The Painlevé analysis demonstrates that established sum of integrable models retains the integrability of each component.
The research also presents a set of rational schemes of trigonometric and hyperbolic functions to derive breather solutions.
The authors also furnish a variety of solitonic solutions and complex solutions as well.
The work formally furnishes algorithms for extending integrable equations that consist of components of a hierarchy.
The paper presents an original work for developing Painlevé integrable model via using components of a hierarchy.
