Articles written in Indian Academy of Sciences Conference Series
Volume 2 All articles Published: 16 September 2019 Article ID 0010 Special
We recall six different analytical methods, namely extended Prelle–Singer procedure, Lie point symmetries, $\lambda$-symmetries, adjoint symmetries, Jacobi last multiplier and Darboux polynomial methods which are used to identify integrability quantifiers of nonlinear ordinary differential equations (ODEs).We point out how these methods are interconnected in the case of two-coupled first-order nonlinear ODEs.We demonstrate the interconnections with an example.
Volume 2 All articles Published: 16 September 2019 Article ID 0011 Special
In this paper, we briefly review a few interesting dynamical aspects and applications of nonlinear $PT$-symmetric systems. Being at the boundary between dissipative and conservative systems, these $PT$-symmetric systems show many interesting characteristics and applications that cannot be seen in the usual dissipative and conservative ones. Among the variety of applications, we here focus on the applicability of $PT$-symmetric systems in unidirectional light transport. This particular application clearly evidences the usefulness of the non-reciprocal nature and symmetry broken phase of a PT-symmetric system and importantly the role of nonlinearities in optics.