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

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

中国物理B ›› 2012, Vol. 21 ›› Issue (3): 30507-030507.doi: 10.1088/1674-1056/21/3/030507

马正义,马松华

收稿日期:2011-06-06 修回日期:2011-07-05 出版日期:2012-02-15 发布日期:2012-02-15
通讯作者: 马正义,mazhengyi_77@yahoo.com.cn E-mail:mazhengyi_77@yahoo.com.cn

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

Ma Zheng-Yi(马正义)^† and Ma Song-Hua(马松华)

College of Mathematics and Physics, Zhejiang Lishui University, Lishui 323000, China

Received:2011-06-06 Revised:2011-07-05 Online:2012-02-15 Published:2012-02-15
Contact: Ma Zheng-Yi,mazhengyi_77@yahoo.com.cn E-mail:mazhengyi_77@yahoo.com.cn
Supported by:
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).

摘要/Abstract

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.

Key words: nonlinear Schrödinger equation, similarity transformation, rational-like solution, rogue wave

中图分类号: (Solitons)

05.45.Yv

03.65.Ge (Solutions of wave equations: bound states)

马正义,马松华. [J]. 中国物理B, 2012, 21(3): 30507-030507.

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[J]. Chin. Phys. B, 2012, 21(3): 30507-030507.

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

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