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

      ADIL JHANGEER NAUMAN RAZA HADI REZAZADEH ALY SEADAWY

      Research Article Volume 94 Published: 18 June 2020 Article ID 0087

    • Fulltext

       

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      Permanent link:
      https://www.ias.ac.in/article/fulltext/pram/094/0087

    • Keywords

       

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

    • 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 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.

    • Author Affiliations

       

      ADIL JHANGEER1 NAUMAN RAZA2 HADI REZAZADEH3 ALY SEADAWY4 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

    • Dates

       
      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

  • Pramana – Journal of Physics | News

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      Posted on July 25, 2019

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