Eur. Phys. J. D 63, 141-148 (2011)
https://doi.org/10.1140/epjd/e2011-20031-6

Regular Article

Nonlinear tunneling effect in the (2+1)-dimensional cubic-quintic nonlinear Schrödinger equation with variable coefficients

¹ School of Sciences, Zhejiang A&F University, Lin’an, Zhejiang 311300, P.R. China
² College of Mathematics and Information Engineering, Jiaxing University, Jiaxing 314001, P.R. China
³ School of Physical Science and Technology, Suzhou University, Suzhou, Jiangsu 215006, P.R. China
⁴ Institute of Nonlinear Physics, Zhejiang Normal University, Jinhua, Zhejiang 321004, P.R. China

^a e-mail: dcq424@126.com

Received: 15 January 2011
Received in final form: 1 March 2011
Published online: 17 May 2011

Abstract

By means of the similarity transformation, we obtain exact solutions of the (2+1)-dimensional generalized nonlinear Schrödinger equation, which describes the propagation of optical beams in a cubic-quintic nonlinear medium with inhomogeneous dispersion and gain. A one-to-one correspondence between such exact solutions and solutions of the constant-coefficient cubic-quintic nonlinear Schrödinger equation exists when two certain compatibility conditions are satisfied. Under these conditions, we discuss nonlinear tunneling effect of self-similar solutions. Considering the fluctuation of the fiber parameter in real application, the exact balance conditions do not satisfy, and then we perform direct numerical analysis with initial 5% white noise for the bright similariton passing through the diffraction barrier and well. Numerical calculations indicate stable propagation of the bright similariton over tens of diffraction lengths.