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Nonlinear self-adjointness, conserved quantities, bifurcation analysis and travelling wave solutions of a family of long-wave unstable lubrication model

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Abstract

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 details of 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.

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Authors and Affiliations

  1. Department of Mathematics, Namal Institute, 30 KM Talagang Road, Mianwali, 42250, Pakistan

    Adil Jhangeer

  2. Department of Mathematics, University of the Punjab, Lahore, Pakistan

    Nauman Raza

  3. Faculty of Engineering Technology, Amol University of Special Modern Technologies, Amol, Iran

    Hadi Rezazadeh

  4. Mathematics Department, Faculty of Science, Taibah University, Al-Madinah Al-Munawarah, Saudi Arabia

    Aly Seadawy

  5. Mathematics Department, Faculty of Science, Beni-Suef University, Beni Suef, Egypt

    Aly Seadawy

Authors
  1. Adil Jhangeer
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  2. Nauman Raza
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  3. Hadi Rezazadeh
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  4. Aly Seadawy
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Correspondence to Adil Jhangeer.

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Jhangeer, A., Raza, N., Rezazadeh, H. et al. Nonlinear self-adjointness, conserved quantities, bifurcation analysis and travelling wave solutions of a family of long-wave unstable lubrication model. Pramana - J Phys 94, 87 (2020). https://doi.org/10.1007/s12043-020-01961-6

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  • DOI: https://doi.org/10.1007/s12043-020-01961-6

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