Travelling wave solutions of the Rosenau equation using exp(±φ(ξ))-expansion method* *Foundation item: Project Supported by Science and Technology Program Fund Project of Guizhou Province, China (Qian Ke He Ji Chu-ZK[2022]021); Universities Key Laboratory of System Modeling and Data Mining in Guizhou Province (No.2023013);The Science and Technology Program of Guizhou Province(No. QKHZC[2023]372);The Science and Research Projects for Universities of Department of

Abstract

The Rosenau equation has been widely used to describe important physical phenomena and dynamic processes in physics, many numerical techniques have been presented in current literature. However, it is typically difficult to obtain exact solutions and analytical methods of this equation. In this paper, the exp(±φ(ξ)) -expansion method is proposed by making full use of the classical Burgers equation, which can be applied to find a large number of travelling wave solutions of the Rosenau equation. These obtained solutions are novel and crucial for explaining exactly certain physical wave phenomena. The method provides an extensive applicability for solving nonlinear evolution partial differential equations.