Two-dimensional accessible solitons in PT-symmetric potentials
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Two-dimensional parity-time (PT) symmetric potentials are introduced, which allow the existence of spatial solitons in the model of the strongly nonlocal nonlinear Schrödinger equation. Two-dimensional accessible solitons are found in the form of solutions separating the radial amplitude, given in terms of Laguerre polynomials, a phase function involving quadratic, linear, and constant phase shifts, and a specific azimuthal modulation function. Shape-preserving solitons are constructed from Laguerre-Gaussian functions containing the self-similar variable and an exponential form of the azimuthal modulation, containing sine and cosine functions, when a suitable PT-symmetric potential is chosen. Interesting soliton profiles and the corresponding PT-symmetric potentials are displayed for different values of the parameters. © Springer Science+Business Media B.V. 2012.
author list (cited authors)
Zhong, W., Belić, M. R., & Huang, T.