R SINUVASAN
Articles written in Pramana – Journal of Physics
Volume 88 Issue 5 May 2017 Article ID 0074 Research Article
Algebraic resolution of the Burgers equation with a forcing term
R SINUVASAN K M TAMIZHMANI P G L LEACH
We introduce an inhomogeneous term, $f (t,x)$, into the right-hand side of the usual Burgers equation and examine the resulting equation for those functions which admit at least one Lie point symmetry. For those functions $f (t,x)$ which depend nontrivially on both $t$ and $x$, we find that there is just one symmetry. If $f$ is a function of only $x$, there are three symmetries with the algebra $sl(2,R)$. When $f$ is a function of only $t$ , there are five symmetries with the algebra $sl(2,R)\oplus_{s} 2A_1$. In all the cases, the Burgers equation is reduced to the equation for a linear oscillator with nonconstant coefficient.
Volume 95 All articles Published: 19 May 2021 Article ID 0085 Reserach Article
Symmetries and integrability of the modified Camassa–Holm equation with an arbitrary parameter
A DURGA DEVI K KRISHNAKUMAR R SINUVASAN P G L LEACH
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.
Volume 95, 2021
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