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

Amjad Hussain; Muhammad Khubaib Zia; Kottakkaran Sooppy Nisar; Velusamy Vijayakumar; Ilyas Khan; Amjad Hussain; Muhammad Khubaib Zia; Kottakkaran Sooppy Nisar; Velusamy Vijayakumar; Ilyas Khan

doi:10.3934/math.2022725

AIMS Mathematics

2022, Volume 7, Issue 7: 13139-13168. doi: 10.3934/math.2022725

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

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

Received: 10 February 2022 Revised: 24 March 2022 Accepted: 01 April 2022 Published: 10 May 2022
MSC : 58D19, 76M60, 37K06, 70H33

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.
- generalized Boussinesq equation,
- Lie symmetry analysis,
- nonlinear self-adjointness,
- $ \left(G^\prime/G, 1/G\right) $ expansion method,
- conservation laws
Citation: Amjad Hussain, Muhammad Khubaib Zia, Kottakkaran Sooppy Nisar, Velusamy Vijayakumar, Ilyas Khan. Lie analysis, conserved vectors, nonlinear self-adjoint classification and exact solutions of generalized $ \left(N+1\right) $-dimensional nonlinear Boussinesq equation[J]. AIMS Mathematics, 2022, 7(7): 13139-13168. doi: 10.3934/math.2022725

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Abstract

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.

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