Using multivariate self-similarity transformation, we construct explicit spatial bright and dark solitary wave solutions of the generalized nonlinear Schrödinger equation with spatially Bessel-modulated nonlinearity and an external potential. Special kinds of explicit solutions, such as periodically breathing bright and dark solitary waves, are discussed in detail. The stability of these solutions is verified by means of direct numerical simulation.
© 2013 Optical Society of America
Original Manuscript: January 17, 2013
Revised Manuscript: March 15, 2013
Manuscript Accepted: March 15, 2013
Published: April 19, 2013
Wei-Ping Zhong, Milivoj R. Belić, and Tingwen Huang, "Solitary waves in the nonlinear Schrödinger equation with spatially modulated Bessel nonlinearity," J. Opt. Soc. Am. B 30, 1276-1283 (2013)