https://doi.org/10.1140/epjp/s13360-021-01073-z
Regular Article
Lie symmetry analysis, optimal system and invariant solutions of (3+1)-dimensional nonlinear wave equation in liquid with gas bubbles
Department of Applied Science and Engineering, Indian Institute of Technology Roorkee, Roorkee, India
Received:
1
September
2020
Accepted:
6
January
2021
Published online:
3
February
2021
In this manuscript, we investigate the (3+1)-dimensional nonlinear wave equation in liquid with gas bubbles. It describes the dynamics of nonlinear waves in hydrodynamics. Liquids with gas bubbles are commonly seen in natural science, engineering, medical science and daily life. The Lie symmetry analysis is used to investigate its vector fields and optimal systems. Moreover, the symmetry reductions and invariant solutions of the equation are obtained based on the optimal systems. Finally, we obtained the exact solutions of (3+1)-dimensional nonlinear wave equation. We showed the physical explanation of obtained solutions by three-dimensional graphically. These newly constructed solutions play an important role in mathematical analysis and other various branches of applied sciences.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2021
