A Comprehensive Study on Symmetry and New Exact Solutions for (3 + 1) – Dimensional Mikhailov-Novikov-Wang Equation
摘要
This article investigates new exact solutions for the (3 + 1)–dimensional Mikhailov-Novikov-Wang equation, an extension of the (1 + 1)–dimensional Mikhailov-Novikov-Wang equation, which is notable for its connection to higher symmetries and the Boussinesq equation, complete integrability. While the Mikhailov-Novikov-Wang equation has been extensively studied and shown to be integrable with multiple soliton solutions, recent research has extended this to higher dimensions. The extended Mikhailov-Novikov-Wang equation has been found to be Painlevé integrable, yielding various soliton solutions such as rational, periodic, and kink-type solitons. Interestingly, while previous literature has primarily focused on soliton solutions, a comprehensive symmetry analysis of the equation remains unexplored to best of our knowledge. Here, we provide thorough exploration of the symmetries of the equation, including both classical and non-classical symmetries. By utilizing these symmetries, we are able to obtain exact solutions and illustrate them graphically, which enhances our comprehension of the dynamics of the equation.