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      Permanent link:
      https://www.ias.ac.in/article/fulltext/pram/095/0085

    • Keywords

       

      Modified Camassa–Holm equation; symmetry; Painlevé test; integrability

    • Abstract

       

      We study the symmetry and integrability of a modified Camassa–Holm equation (MCH), with an arbitrary parameter $k$, of the form $u_t + k(u − u_{xx})^{2}u_x − u_{xxt} + (u^2 − u_x^2)(u_x − u_{xxx} ) = 0.$ The commutator table and adjoint representation of the symmetries are presented to construct one-dimensional optimal system. By using the one-dimensional optimal system, we reduce the order or number of independent variables of the above equation and also we obtain interesting novel solutions for the reduced ordinary differential equations. Finally, we apply the Painlevé test to the resultant nonlinear ordinary differential equation and it is observed that the equation is integrable.

    • Author Affiliations

       

      A DURGA DEVI1 K KRISHNAKUMAR2 R SINUVASAN3 P G L LEACH4

      1. Department of Physics, Srinivasa Ramanujan Centre, SASTRA Deemed to be University, Kumbakonam 612 001, India
      2. Department of Mathematics, Srinivasa Ramanujan Centre, SASTRA Deemed to be University, Kumbakonam 612 001, India
      3. Department of Mathematics, VIT-AP University, Amaravathi 522 237, India
      4. Department of Mathematics, Durban University of Technology, P.O. Box 1334, Durban 4000, Republic of South Africa

    • Dates

       
      Published
      19 May 2021
      Manuscript received
      5 May 2020
      Manuscript revised
      12 August 2020
      Accepted
      30 December 2020
      Final version published online
      19 May 2021

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