Physical multiple shock solutions to the integrability of linear structures of Burgers hierarchy

Abstract

This work is concerned with the formation of linear structures of components of Burgers' hierarchy. The integrability of some linear systems of two or more parts is investigated. A linear arrangement of five elements is studied by using the Painlevé analysis. The simplified Hirota's method provides a trustworthy cure for the proposed linear design of the five components, where multiple kink solutions are formally derived for this constructed system. Our findings can help many researchers interested in fluid mechanics and plasma physics.