Nonlocal Symmetries for Bilinear Equations and Their Applications

doi:10.1111/j.1467-9590.2009.00435.x

	Nonlocal Symmetries for Bilinear Equations and Their Applications
	Hu, Xing-Biao; Lou, Sen-Yue; Qian, Xian-Min
	2009-04-01
发表期刊	STUDIES IN APPLIED MATHEMATICS
ISSN	0022-2526
卷号	122 期号:3 页码:305-324
摘要	In this paper, nonlocal symmetries for the bilinear KP and bilinear BKP equations are re-studied. Two arbitrary parameters are introduced in these nonlocal symmetries by considering gauge invariance of the bilinear KP and bilinear BKP equations under the transformation . By expanding these nonlocal symmetries in power series of each of two parameters, we have derived two types of bilinear NKP hierarchies and two types of bilinear NBKP hierarchies. An impressive observation is that bilinear positive and negative KP (NKP) and BKP hierarchies may be derived from the same nonlocal symmetries for the KP and BKP equations. Besides, as two concrete examples, we have derived bilinear BAcklund transformations for t(-2)-flow of the NKP hierarchy and t(-1)-flow of the NBKP hierarchy. All these results have made it clear that more nice integrable properties would be found for these obtained NKP hierarchies and NBKP hierarchies. Because KP and BKP hierarchies have played an essential role in soliton theory, we believe that the bilinear NKP and NBKP hierarchies will have their right place in this field.
DOI	10.1111/j.1467-9590.2009.00435.x
语种	英语
资助项目	National Natural Science Foundation of China[10771207] ; National Natural Science Foundation of China[10735030] ; National Natural Science Foundation of China[90503006]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000264819400006
出版者	WILEY-BLACKWELL PUBLISHING, INC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/8258
专题	计算数学与科学工程计算研究所
通讯作者	Hu, Xing-Biao
作者单位	Chinese Acad Sci, Acad Math & Syst Sci, LSEC, ICMSEC, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Hu, Xing-Biao,Lou, Sen-Yue,Qian, Xian-Min. Nonlocal Symmetries for Bilinear Equations and Their Applications[J]. STUDIES IN APPLIED MATHEMATICS,2009,122(3):305-324.
APA	Hu, Xing-Biao,Lou, Sen-Yue,&Qian, Xian-Min.(2009).Nonlocal Symmetries for Bilinear Equations and Their Applications.STUDIES IN APPLIED MATHEMATICS,122(3),305-324.
MLA	Hu, Xing-Biao,et al."Nonlocal Symmetries for Bilinear Equations and Their Applications".STUDIES IN APPLIED MATHEMATICS 122.3(2009):305-324.