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	A time-splitting spectral method for three-wave interactions in media with competing quadratic and cubic nonlinearities
	Bao, Weizhu ; Zheng, Chunxiong
	2010-05-06 ; 2010-05-06
关键词	nonlinear optics three-wave time-splitting spectral method energy continuous wave soliton GROSS-PITAEVSKII EQUATION SCHRODINGER-EQUATION SOLITONS EVOLUTION Physics, Mathematical
中文摘要	This paper introduces an extension of the time-splitting spectral (TSSP) method for solving a general model of three-wave optical interactions, which typically arises from nonlinear optics, when the transmission media has competing quadratic and cubic nonlinearities. The key idea is to formulate the terms related to quadratic and cubic nonlinearities into a Hermitian matrix in a proper way, which allows us to develop an explicit and unconditionally stable numerical method for the problem. Furthermore, the method is spectral accurate in transverse coordinates and second-order accurate in propagation direction, is time reversible and time transverse invariant, and conserves the total wave energy (or power or the norm of the solutions) in discretized level. Numerical examples are presented to demonstrate the efficiency and high resolution of the method. Finally the method is applied to study dynamics and interactions between three-wave solitons and continuous waves in media with competing quadratic and cubic nonlinearities in one dimension (1D) and 2D.
语种	英语 ; 英语
出版者	GLOBAL SCIENCE PRESS ; WANCHAI ; ROOM 2303, OFFICER TOWER, CONVENTION PLAZA, 1 HARBOUR ROAD, WANCHAI, HONG KONG 00000, PEOPLES R CHINA
内容类型	期刊论文
源URL	[http://hdl.handle.net/123456789/13823]
专题	清华大学
推荐引用方式 GB/T 7714	Bao, Weizhu,Zheng, Chunxiong. A time-splitting spectral method for three-wave interactions in media with competing quadratic and cubic nonlinearities[J],2010, 2010.
APA	Bao, Weizhu,&Zheng, Chunxiong.(2010).A time-splitting spectral method for three-wave interactions in media with competing quadratic and cubic nonlinearities..
MLA	Bao, Weizhu,et al."A time-splitting spectral method for three-wave interactions in media with competing quadratic and cubic nonlinearities".(2010).

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