Cieśliński J.Extended Lie point symmetries. The case of inhomogeneous NLS equation, talk at The Workshop on Integrable Nonlinear Equations, 18-24 October 2015, Mikulov, Czech Republic (abstract)

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Speaker: Jan Cieśliński

Title: Extended Lie point symmetries. The case of inhomogeneous NLS equation

Abstract:
We present a notion of extended Lie point symmetries, i.e., symmetries of a family of differential equations, parameterized by one or more functions. Performing symmetry analysis we treat these functions as additional variables. Extended Lie point symmetries are computed as point symmetries with respect to all variables except those additional ones (they can transform into any function of the same type). One case, namely inhomogeneous Nonlinear Schrödinger equation, is of special interest, because applying this approach we obtain a group of nonlocal symmetries in an explicit form. The group parameter is related to the spectral parameter of the associated (nonisospectral) Lax pair. The main result is old but, in my opinion, a full interpretation of this phenomenon is still missing. Another challenge is to find other interesting or useful examples.

Slides: Cieśliński J.Extended Lie point symmetries. The case of inhomogeneous NLS equation (presentation at The Workshop on Integrable Nonlinear Equations, 18-24 October 2015, Mikulov, Czech Republic).pdf