Document Type

Conference Paper


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Applied mathematics

Publication Details

This is a conference proceedings report based upon a talk given at the Annual Meeting of Bulgarian Branch of SIAM that took place in Sofia, Bulgaria in December, 2013. Subsequently published in the the Conference Proceedings published by Cambridge Scholars Publishing.


We consider a nonlocal nonlinear Schr\"odinger equation recently proposed by Ablowitz and Musslimani as a theoretical model for wave propagation in {\it PT}-symmetric coupled wave-guides and photonic crystals. This new equation is integrable by means of inverse scattering method, i. e. it possesses a Lax pair, infinite number of integrals of motion and exact solutions. We aim to describe here some of the basic properties of the nonlocal Schr\"odinger equation and its scattering operator. In doing this we shall make use of methods alternative to those applied by Ablowitz and Musslimani which seem to be better suited for treating possible multicomponent generalizations.



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