An exact (2+1)-dimensional optical soliton with spatially modulated nonlinearity and an external potential
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EDP Sciences, Societ Italiana di Fisica, Springer-Verlag. An exact (2 + 1)-dimensional spatial optical soliton of the nonlinear Schrdinger 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 Schrdinger 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.
EUROPEAN PHYSICAL JOURNAL D
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Zhong, Wei-Ping||Belić, Milivoj