Nonlocal symmetries and negative hierarchies related to bilinear Bäcklund transformation

doi:10.1088/1674-1056/24/3/030201

中国物理B ›› 2015, Vol. 24 ›› Issue (3): 30201-030201.doi: 10.1088/1674-1056/24/3/030201

• GENERAL • 下一篇

Nonlocal symmetries and negative hierarchies related to bilinear Bäcklund transformation

胡晓瑞^a, 陈勇^b

a Department of Applied Mathematics, Zhejiang University of Technology, Hangzhou 310023, China;
b Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai 200062, China

收稿日期:2014-07-22 修回日期:2014-10-15 出版日期:2015-03-05 发布日期:2015-03-05
基金资助:
Project supported by the Natural Science Foundation of Zhejiang Province, China (Grant No. LQ13A010014), the National Natural Science Foundation of China (Grant Nos. 11326164, 11401528, and 11275072), and the Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20120076110024).

Nonlocal symmetries and negative hierarchies related to bilinear Bäcklund transformation

Hu Xiao-Rui (胡晓瑞)^a, Chen Yong (陈勇)^b

a Department of Applied Mathematics, Zhejiang University of Technology, Hangzhou 310023, China;
b Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai 200062, China

Received:2014-07-22 Revised:2014-10-15 Online:2015-03-05 Published:2015-03-05
Contact: Hu Xiao-Rui E-mail:baqi2002@163.com
Supported by:
Project supported by the Natural Science Foundation of Zhejiang Province, China (Grant No. LQ13A010014), the National Natural Science Foundation of China (Grant Nos. 11326164, 11401528, and 11275072), and the Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20120076110024).

摘要/Abstract

摘要：

In this paper, nonlocal symmetries defined by bilinear Bäcklund transformation for bilinear potential KdV (pKdV) equation are obtained. By introducing an auxiliary variable which just satisfies the Schwartzian form of KdV (SKdV) equation, the nonlocal symmetry is localized and the Levi transformation is presented. Besides, based on three different types of nonlocal symmetries for potential KdV equation, three sets of negative pKdV hierarchies along with their bilinear forms are constructed. An impressive result is that the coefficients of the third type of (bilinear) negative pKdV hierarchy (N>0) are variable, which are obtained via introducing an arbitrary parameter by considering the translation invariance of the pKdV equation.

关键词: nonlocal symmetry, bilinear Bä, cklund transformation, finite transformation, negative hierarchy

Abstract:

Key words: nonlocal symmetry, bilinear Bä, cklund transformation, finite transformation, negative hierarchy

中图分类号: (Integrable systems)

02.30.Ik

02.20.-a (Group theory) 04.20.Jb (Exact solutions)

胡晓瑞, 陈勇. Nonlocal symmetries and negative hierarchies related to bilinear Bäcklund transformation[J]. 中国物理B, 2015, 24(3): 30201-030201.

Hu Xiao-Rui (胡晓瑞), Chen Yong (陈勇). Nonlocal symmetries and negative hierarchies related to bilinear Bäcklund transformation[J]. Chin. Phys. B, 2015, 24(3): 30201-030201.

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Nonlocal symmetries and negative hierarchies related to bilinear Bäcklund transformation

Nonlocal symmetries and negative hierarchies related to bilinear Bäcklund transformation

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