• Symmetries and integrability of the modified Camassa–Holm equation with an arbitrary parameter

• # Fulltext

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

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

• # Pramana – Journal of Physics

Volume 95, 2021
All articles
Continuous Article Publishing mode

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019