• Lie symmetry analysis, abundant exact solutions and dynamics of multisolitons to the (2 + 1)-dimensional KP-BBM equation

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    • Keywords

       

      Exact solutions; solitons; Lie symmetry analysis; generalised exponential rational function method; (2 + 1)-dimensional Kadomtsev–Petviashvili-Benjamin–Bona–Mahony equation.

    • Abstract

       

      In the present article, our main aim is to construct abundant exact solutions for the (2+1)-dimensional Kadomtsev–Petviashvili-Benjamin–Bona–Mahony (KP-BBM) equation by using two powerful techniques, the Lie symmetry method and the generalised exponential rational function (GERF) method with the help of symbolic computations via Mathematica. Firstly, we have derived infinitesimals, geometric vector fields, commutation relations and optimal system. Therefore, the KP-BBM equation is reduced into several nonlinear ODEs under two stages of symmetry reductions. Furthermore, abundant solutions are obtained in different shapes of single solitons, solitary wave solutions, quasiperiodic wave solitons, elastic multisolitons, dark solitons and bright solitons, which are more relevant, meaningful and useful to describe physical phenomena due to the existence of free parameters and constants. All these generated exact soliton solutions are new and completely different from the previous findings. Moreover, the dynamical behaviour of the obtained exact closed-form solutions is analysed graphically by their 3D, 2D-wave profiles and the corresponding density plots by using the mathematical software, which will be comprehensively used to explain complex physical phenomena in the fields of nonlinear physics, plasma physics, optical physics, mathematical physics, nonlinear dynamics, etc.

    • Author Affiliations

       

      SACHIN KUMAR1 DHARMENDRA KUMAR2 HARSHA KHARBANDA1

      1. Department of Mathematics, Faculty of Mathematical Sciences, University of Delhi, Delhi 110 007, India
      2. Department of Mathematics, SGTB Khalsa College, University of Delhi, Delhi 110 007, India
    • Dates

       
  • Pramana – Journal of Physics | News

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