Eur. Phys. J. D (2014) 68: 331
https://doi.org/10.1140/epjd/e2014-50580-9

Regular Article

An exact (2 + 1)-dimensional optical soliton with spatially modulated nonlinearity and an external potential

¹ Department of Electronic and Information Engineering, Shunde Polytechnic, Guangdong Province, Shunde 528300, P.R. China
² Texas A&M University at Qatar, P.O. Box 23874, Doha, Qatar
³ Institute of Physics, University of Belgrade, P.O. Box 68, 11001 Belgrade, Serbia

^a e-mail: zhongwp6@126.com

Received: 6 August 2014
Received in final form: 4 September 2014
Published online: 3 November 2014

Abstract

An exact (2 + 1)-dimensional spatial optical soliton of the nonlinear Schrödinger equation with a spatially modulated nonlinearity and a special external potential is discovered in an inhomogeneous nonlinear medium, by utilizing the similarity transformation. Exact analytical solutions are constructed by the products of Whittaker functions and the bright and dark soliton solutions of the standard stationary nonlinear Schrödinger equation. Some examples of such composed solutions are given, in which these spatial solitons display different localized structures. Numerical calculation shows that the soliton is stable in propagating over long distances, thus also confirming the validity of the exact solution.