Lie analysis, conserved vectors, nonlinear self-adjoint classification and exact solutions of generalized $ \left(N+1\right) $-dimensional nonlinear Boussinesq equation

AIMS Mathematics

Amjad Hussain¹  Muhammad Khubaib Zia¹  Kottakkaran Sooppy Nisar²  Velusamy Vijayakumar³  Ilyas Khan⁴ 

[1] 1. Department of Mathematics, Quaid-I-Azam University 45320, Islamabad, Pakistan;2. Department of Mathematics, College of arts and sciences, Prince Sattam bin Abdulaziz University, Wadi Aldawaser 11991, Saudi Arabia;3. Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore -632 014, Vellore, Tamilnadu, India;4. Department of Mathematics, College of Science Al-Zulfi, Majmaah University, Al-Majmaah 11952, Saudi Arabia;

关键词: generalized boussinesq equation;    lie symmetry analysis;    nonlinear self-adjointness;    $ \left(g^\prime/g;    1/g\right) $ expansion method;    conservation laws;   

DOI  :  10.3934/math.2022725

来源: DOAJ

【 摘 要 】

In this article, the generalized $ \left(N+1\right) $-dimensional nonlinear Boussinesq equation is analyzed via Lie symmetry method. Lie point symmetries of the considered equation and accompanying invariant groups are computed. After transforming the equation into a nonlinear ordinary differential equation (ODE), analytical solutions of various types are obtained using the $ \left(G^\prime/G, 1/G\right) $ expansion method. The concept of nonlinear self-adjointness is used in order to determine nonlocal conservation laws of the equation in lower dimensions. By selecting the appropriate parameter values, the study provides a graph of the solutions to the equation under study.

【 授权许可】

Unknown