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Z. Naturforsch. 66a, 500 – 506
(2011)
doi:10.5560/ZNA.2011-0007
Coherent Structures in the (2 + 1)-Dimensional Nonlinear Schrödinger Equation with Time-Varying Coefficients
1 Department of Mathematics, Lishui University, Zhejiang Lishui 323000, P.R. China
2 Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, P.R. China
Received December 27, 2010 / revised April 17, 2011
Reprint requests to: Z.-Y. M.; E-mail:
mazhengyi_77@yahoo.com.cn
Analytical solutions in terms of rational-like functions are derived for the (2 + 1)-dimensional nonlinear Schrödinger equation with time-varying coefficients using the similarity transformation and direct ansatz. By applying specific time-modulated nonlinearities, dispersions, and potentials, the dynamics of the solutions can be controlled. As a result, abundant wave structures are exhibited through chosen three types of elementary functions.
Key words: Nonlinear Schrödinger Equation; Similarity Transformation; Rational-Like Solution; Coherent Structure.
PACS numbers: 03.65.Ge; 05.45.Yv