Physical explanations of infinite symmetries of Sharma-Tasso-Olver equation

Abstract

The Sharma-Tasso-Olver (STO) equation is characterized by an infinite number of symmetries; however, the physical implications of these symmetries have not been well established. Recently, a conjecture was proposed to illustrate the physical explanations of the infinite symmetries associated with several well-known equations. Inspired by the insights derived from this conjecture, this manuscript discusses the physical explanations of the infinite symmetries related to the n-soliton solutions and the two-wave complexiton solution of the STO equation. Our findings reveal that the K-symmetries correspond to symmetries associated with wave center translations, while the τ-symmetries encompass wave number translation symmetries as well as center translation symmetries applicable to both n-soliton and two-wave complexiton solutions. Furthermore, these results suggest a certain incompleteness inherent of the infinitely many symmetries. Additionally, we construct the n-wave solutions for the STO equation utilizing the framework provided by the conjecture.