Analytical solutions and rogue waves in (3+1)-dimensional nonlinear Schrödinger equation

doi:10.1088/1674-1056/21/3/030507

Abstract Analytical solutions in terms of rational-like functions are presented for a (3+1)-dimensional nonlinear Schrödinger equation with time-varying coefficients and a harmonica potential using the similarity transformation and a direct ansatz. Several free functions of time t are involved to generate abundant wave structures. Three types of elementary functions are chosen to exhibit the corresponding nonlinear rogue wave propagations.

Keywords: nonlinear Schrödinger equation similarity transformation rational-like solution rogue wave

Received: 06 June 2011
Revised: 05 July 2011
Accepted manuscript online:

PACS:	05.45.Yv	(Solitons)
	03.65.Ge	(Solutions of wave equations: bound states)

Fund: Project supported by the National Natural Science Foundation of China (Grant No. 10772110) and the Natural Science Foundation of Zhejiang Province, China (Grant Nos. Y606049, Y6090681, and Y6100257).

Corresponding Authors: Ma Zheng-Yi,mazhengyi_77@yahoo.com.cn
E-mail: mazhengyi_77@yahoo.com.cn

Cite this article:

Ma Zheng-Yi(马正义) and Ma Song-Hua(马松华) Analytical solutions and rogue waves in (3+1)-dimensional nonlinear Schrödinger equation 2012 Chin. Phys. B 21 030507

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