CONDITIONAL SIMILARITY REDUCTION APPROACH: JIMBO－MIWA EQUATION

doi:10.1088/1009-1963/10/10/303

中国物理B ›› 2001, Vol. 10 ›› Issue (10): 897-901.doi: 10.1088/1009-1963/10/10/303

CONDITIONAL SIMILARITY REDUCTION APPROACH: JIMBO－MIWA EQUATION

楼森岳¹, 唐晓艳²

(1)Department of Physics, Ningbo University, Ningbo 315211, China; Department of Physics, Shanghai Jiaotong University, Shanghai 200030, China; (2)Department of Physics, Shanghai Jiaotong University, Shanghai 200030, China

收稿日期:2000-07-20 修回日期:2001-05-15 出版日期:2001-10-15 发布日期:2005-06-12
基金资助:
Project supported by the National Natural Science Foundation for Outstanding Young Scientists of China (Grant No. 19925522), by the Doctoral Program Foundation of Institutions of Higher Education of China (Grant No. 2000024832) and by the Natural Science Foundation of Zheijiang Province, China.

CONDITIONAL SIMILARITY REDUCTION APPROACH: JIMBO--MIWA EQUATION

Lou Sen-yue (楼森岳)^ab, Tang Xiao-yan (唐晓艳)^b

^a Department of Physics, Ningbo University, Ningbo 315211, China; ^b Department of Physics, Shanghai Jiaotong University, Shanghai 200030, China

Received:2000-07-20 Revised:2001-05-15 Online:2001-10-15 Published:2005-06-12
Supported by:
Project supported by the National Natural Science Foundation for Outstanding Young Scientists of China (Grant No. 19925522), by the Doctoral Program Foundation of Institutions of Higher Education of China (Grant No. 2000024832) and by the Natural Science Foundation of Zheijiang Province, China.

摘要/Abstract

摘要： The direct method developed by Clarkson and Kruskal (1989 J. Math. Phys. 30 2201) for finding the symmetry reductions of a nonlinear system is extended to find the conditional similarity solutions. Using the method of the Jimbo－Miwa (JM) equation, we find that three well-known (2+1)-dimensional models－the asymmetric Nizhnik--Novikov－Veselov equation, the breaking soliton equation and the Kadomtsev-Petviashvili equation－can all be obtained as the conditional similarity reductions of the JM equation.

Abstract: The direct method developed by Clarkson and Kruskal (1989 J. Math. Phys. 30 2201) for finding the symmetry reductions of a nonlinear system is extended to find the conditional similarity solutions. Using the method of the Jimbo－Miwa (JM) equation, we find that three well-known (2+1)-dimensional models－the asymmetric Nizhnik--Novikov--Veselov equation, the breaking soliton equation and the Kadomtsev-Petviashvili equation－can all be obtained as the conditional similarity reductions of the JM equation.

Key words: conditional similarity reductions, Jimbo－Miwa equation, Kadomtsev－Petviashvili equation, breaking soliton equation, asymmetric Nizhnik－Novikov－Veselov equation

中图分类号: (Solitons)

05.45.Yv

03.75.Lm (Tunneling, Josephson effect, Bose-Einstein condensates in periodic potentials, solitons, vortices, and topological excitations)

楼森岳, 唐晓艳. CONDITIONAL SIMILARITY REDUCTION APPROACH: JIMBO－MIWA EQUATION[J]. 中国物理B, 2001, 10(10): 897-901.

Lou Sen-yue (楼森岳), Tang Xiao-yan (唐晓艳). CONDITIONAL SIMILARITY REDUCTION APPROACH: JIMBO--MIWA EQUATION[J]. Chinese Physics, 2001, 10(10): 897-901.

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CONDITIONAL SIMILARITY REDUCTION APPROACH: JIMBO－MIWA EQUATION

CONDITIONAL SIMILARITY REDUCTION APPROACH: JIMBO--MIWA EQUATION

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