TRACKING DOWN LOCALIZED MODES IN PT-SYMMETRIC HAMILTONIANS UNDER THE INFLUENCE OF A COMPETING NONLINEARITY

Authors

  • Bijan Bagchi Department of Applied Mathematics, University of Calcutta, 92 Acharya Prafulla Chandra Road, Kolkata-700 009
  • Subhrajit Modak Department of Physical Science, Indian Institute of Science, Education and Research (Kolkata), Mohanpur, West Bengal 741 252
  • Prasanta K. Panigrahi Department of Physical Science, Indian Institute of Science, Education and Research (Kolkata), Mohanpur, West Bengal 741 252

DOI:

https://doi.org/10.14311/AP.2014.54.0079

Abstract

The relevance of parity and time reversal (PT)-symmetric structures in optical systems has been known for some time with the correspondence existing between the Schrödinger equation and the paraxial equation of diffraction, where the time parameter represents the propagating distance and the refractive index acts as the complex potential. In this paper, we systematically analyze a normalized form of the nonlinear Schrödinger system with two new families of PT-symmetric potentials in the presence of competing nonlinearities. We generate a class of localized eigenmodes and carry out a linear stability analysis on the solutions. In particular, we find an interesting feature of bifurcation characterized by the parameter of perturbative growth rate passing through zero, where a transition to imaginary eigenvalues occurs.

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Published

2014-04-30

Issue

Vol. 54 No. 2 (2014)

Section

Articles

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How to Cite

Bagchi, B., Modak, S., & Panigrahi, P. K. (2014). TRACKING DOWN LOCALIZED MODES IN PT-SYMMETRIC HAMILTONIANS UNDER THE INFLUENCE OF A COMPETING NONLINEARITY. Acta Polytechnica, 54(2), 79-84. https://doi.org/10.14311/AP.2014.54.0079