SAMS Subject Classification Number: 3

We perform classical symmetry reductions of a bi-dimensional nonlinear wave equation that is very important in modelling diverse occurrences with applications in engineering physics, fluid dynamics, cosmology, plasma physics and so on [1–6]. This leads to various invariant and solitary wave solutions of interests. In addition, a steady-state series solution of the model is found. Besides, the associated conserved vectors [4–6] of the understudy equation are also investigated, thus yielding some vectors of note in physical sciences.

[1] N. Dimakis, A. Giacomini, S. Jamal, G. Leon, Noether symmetries and stability of ideal gas solutions in Galileon cosmology, Physical Review D, 95 (2017) 064031.

[2] W.F. Ames, Nonlinear Partial Differential Equations in Engineering, Academic Press, New York, 1965.

[3] S.J. Chen, Y.H. Yin, W.X. Ma, X, Lü, Abundant exact solutions and interaction phenomena of the (2+1)-dimensional YTSF equation, Analysis and Mathematical Physics, 9 (2019) 2329–2344.

[4] O.D. Adeyemo, C.M. Khalique, Analytic solutions and conservation laws of a (2+1)-dimensional generalized Yu-Toda-Sasa-Fukuyama equation, Chinese Journal of Physics, 77 (2021) 927–744.

[5] O.D. Adeyemo, L. Zhang, C.M. Khalique, Bifurcation theory, Lie group-invariant solutions and conservation laws of a generalized (2+1)-dimensional BK equation Type II in plasma physics and fluid mechanics, Mathematics, 10 (2022) 2391.

[6] A.A. Zaidi, M.D. Khan,I. Naeem, Conservation Laws and Exact Solutions of Generalized Nonlinear System and Nizhink-Novikov-Veselov Equation, Mathematical Problems in Engineering, 2018 (2018).