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Nonlinear self-adjointness; bifurcation analysis; analytic solutions; long-wave unstable lubrication model

The paper investigates a class of long-wave unstable lubrication model using Lie theory. A nonlinear self-adjoint classification of the considered equation is carried out. Without having to go into microscopic detailsof the physical aspects, non-trivial conservation laws are computed. Then, minimal set of Lie point symmetries of the discussed model is classified up to one-dimensional conjugacy classes which are further utilised one by one to construct the similarity variables to reduce the dimension of the considered model. After that, all possible phase trajectories are classified with respect to the parameters of the equation. Some travelling wave and kink-wave solutions are also showed and graphical representations are displayed to depict their propagation.

ADIL JHANGEER¹ NAUMAN RAZA² HADI REZAZADEH³ ALY SEADAWY^{4 5}

1. Department of Mathematics, Namal Institute, 30 KM Talagang Road, Mianwali 42250, Pakistan
2. Department of Mathematics, University of the Punjab, Lahore, Pakistan
3. Faculty of Engineering Technology, Amol University of Special Modern Technologies, Amol, Iran
4. Mathematics Department, Faculty of Science, Taibah University, Al-Madinah Al-Munawarah, Saudi Arabia
5. Mathematics Department, Faculty of Science, Beni-Suef University, Beni Suef, Egypt

Published

18 June 2020

Manuscript received

19 September 2019

Manuscript revised

14 March 2020

Accepted

9 April 2020

Early published

Unedited version published online

Final version published online

16 June 2020