Articles written in Pramana – Journal of Physics
Volume 85 Issue 5 November 2015 pp 807-821
Systematic analytic methods of deriving integrable mappings from integrable nonlinear ordinary differential, differential-difference and lattice equations are presented. More specifically, we explain how to derive integrable mappings through four different techniques namely,
Lax pair approach,
periodic reduction of integrable nonlinear partial difference equations and
construction of sufficient number of integrals of motion.
The applicability of methods have been illustrated through Ricatti equation, a scalar second-order nonlinear ordinary differential equation with cubic nonlinearity, 2- and 3-coupled second-order nonlinear ordinary differential equations with cubic nonlinearity, lattice equations of Korteweg–de Vries, modified Korteweg–deVries and sine-Gordon types.
Volume 85 Issue 5 November 2015 pp 849-860
A systematic method is given to derive Lie point symmetries of time-fractional partial differential equation with Riemann–Liouville fractional derivative and its applicability illustrated through
time-fractional diffusive equation and
time-fractional cylindrical Korteweg–de Vries equation.
Using the Lie point symmetries obtained, we show that each of them has been transformed into ordinary differential equation of fractional order with a new independent variable. We also explain how exact or invariant solutions can be derived from the obtained point symmetries.
Volume 96, 2022
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