THE GEOMETRIC MEANING OF THE RICCATI EQUATION RELATED TO SINE-GORDON EQUATION

WU Yong-Shi; GE Mo-Lin

近期发现有不法分子冒充我刊与作者联系，借此进行欺诈等不法行为，请广大作者加以鉴别，如遇诈骗行为，请第一时间与我刊编辑部联系确认（《中国物理C》（英文）编辑部电话：010-88235947,010-88236950），并作报警处理。

本刊再次郑重声明：

（1）本刊官方网址为cpc.ihep.ac.cn和https://iopscience.iop.org/journal/1674-1137

（2）本刊采编系统作者中心是投稿的唯一路径，该系统为ScholarOne远程稿件采编系统，仅在本刊投稿网网址（https://mc03.manuscriptcentral.com/cpc）设有登录入口。本刊不接受其他方式的投稿，如打印稿投稿、E-mail信箱投稿等，若以此种方式接收投稿均为假冒。

（3）所有投稿均需经过严格的同行评议、编辑加工后方可发表，本刊不存在所谓的“编辑部内部征稿”。如果有人以“编辑部内部人员”名义帮助作者发稿，并收取发表费用，均为假冒。

《中国物理C》（英文）编辑部

2024年10月30日

Chinese Physics C> 1983, Vol. 7> Issue(5) : 560-564

THE GEOMETRIC MEANING OF THE RICCATI EQUATION RELATED TO SINE-GORDON EQUATION

WU Yong-Shi ^, ,
GE Mo-Lin

Abstract
HTML
Reference
Related

PDF

Abstract：
The geometric meaning of the Riccati equation related to the structure of space is discussed. It is shown that the Riccati equation satisfied by the stereographic projection is essentially the structure equation of space.

References

[1]

有关Backlund变换的总结见高玲丽, 广州基本粒子物理理论会议文集(1980).变换性质及与手征场的关系见:K. Pohlmeyer, Cmmun. Math. Phys., 96(1976), 207.[2] V. E. Zakharov and A. B. Shabat, JETP 34(1972), 62.[3] R. Sasaki, Nucl. Phys., B154(1979), 343.[4] 侯伯元, 在上海广义相对论精确解讨论班上的报告(1982).[5] L. P. Eisenhart, "A Treatise on the Differential Geometry of Curves and Surfaces" (1949).[6] 葛墨林, 段一士, 高能物理与核物理, 4(1980),173.[7] 侯伯宇、段一士, 葛墨林, 物理学报, 25(1976),519.

[1]	WANG Jian-Hua , LI Kang , Dulat Sayipjamal , . Klein-Gordon oscillators in noncommutative phase space. Chinese Physics C, 2008, 32(10): 803-806. doi: 10.1088/1674-1137/32/10/007
[2]	ZHANG Ai-Ping , QIANG Wen-Chao . Exact Bound Solution of the Klein-Gordon Equation and the Dirac Equation with Rosen-MorseⅡ Potential. Chinese Physics C, 2007, 31(11): 1027-1031.
[3]	YAN Jun , TAO Bi-You . A Electric Sine-Gordon Soliton Solution in Two-Dimensional Dilaton Gravity Model. Chinese Physics C, 2003, 27(9): 767-769.
[4]	Medina Ablikim , Edward Corrigan . Boundary Reflection Factor of the Supersymmetric Sinh-Gordon Model. Chinese Physics C, 2002, 26(S1): 47-53.
[5]	LI Xi-Guo , Marcello Baldo , SONG Jian-Jun , LIU Fang . Diffusion Equations in Lie Group Manifold. Chinese Physics C, 2001, 25(1): 86-88.
[6]	HUANG Shi-Zhong , RUAN Tu-Nan , WU Ning , ZHENG Zhi-Peng . Bargmann-Wigner Equation and High Spin Field Equations. Chinese Physics C, 2001, 25(11): 1058-1064.
[7]	WANG AnMin , RUAN TuNan . Relativistic Space-Like Equation. Chinese Physics C, 2000, 24(6): 495-504.
[8]	MING ZhaoYu , ZHANG FengShou , CHEN LieWen , ZHU ZhiYuan , ZHAN WenLong , GUO ZhongYan , XIAO GuoQing . Isospin Dependent Boltzmann-Langevin Equation and the Production Cross Section of ¹⁹Na. Chinese Physics C, 2000, 24(7): 656-661.
[9]	Huang Wenhui , Wang Guangwei . Numerical Solution for Vlasov Equation. Chinese Physics C, 1999, 23(12): 1216-1222.
[10]	Zhang Fengshou , Chen Liewen . An Isospin-Dependent Nuclear Equation of State. Chinese Physics C, 1999, 23(12): 1190-1196.
[11]	Zheng Xiaoping , Li Jiarong . Non-Abelian Plasmons and Their Kinectic Equation. Chinese Physics C, 1998, 22(1): 34-40.
[12]	LI Fu-Bin . A Geometrical Formulation Approach of the Generalized Coagulation Equations with Fragmentation Mechanism. Chinese Physics C, 1992, 16(9): 790-793.
[13]	HU Zhan-Ning . The q-Deformed KdV Equation. Chinese Physics C, 1991, 15(8): 765-768.
[14]	SU Jun-Chen , WU Shi-Shu . GORDON DECOMPOSITIONS FOR γ-TYPE MATRICES AND SOME OF THEIR APPLICATIONS. Chinese Physics C, 1987, 11(5): 644-652.
[15]	DAI An-Ying . LEVINSON'S THEOREM FOR KLEIN-GORDON EQUATIONS WITH POTENTIAL TAILS. Chinese Physics C, 1987, 11(5): 620-628.
[16]	SHI Jian-Min . INTEGRABILITY PROPERTY AND GEOMETRIC INTERPRETATION OF CYLINDRICAL EINSTEIN-EQUATION. Chinese Physics C, 1987, 11(2): 167-174.
[17]	HUANG Nian-Ning . ON THE ONE-SOLITON SOLUTIONS OT SUPER-GORDON EGUATION. Chinese Physics C, 1985, 9(3): 382-384.
[18]	RUAN TU-NAN , ZHU XI-QUAN , HE ZUO-XIU , QING CHENG-RUI , ZHAO WEI-QIN . RELATIVISTIC EQUAL-TIME EQUATION (Ⅰ). Chinese Physics C, 1981, 5(4): 393-404.
[19]	ZHUO YI-ZHONG , WU XI-ZHEN . MASTER EQUATIONS FOR COUPLING SYSTEM. Chinese Physics C, 1979, 3(4): 501-510.
[20]	HSXJ KUNG-NGOU . MASTER EQUATION FOR QUANTUM SYSTEMS. Chinese Physics C, 1978, 2(4): 359-367.

Access

Get Citation

WU Yong-Shi and GE Mo-Lin. THE GEOMETRIC MEANING OF THE RICCATI EQUATION RELATED TO SINE-GORDON EQUATION[J]. Chinese Physics C, 1983, 7(5): 560-564.

WU Yong-Shi and GE Mo-Lin. THE GEOMETRIC MEANING OF THE RICCATI EQUATION RELATED TO SINE-GORDON EQUATION[J]. Chinese Physics C, 1983, 7(5): 560-564. shu

RIS(for EndNote,Reference Manager,ProCite)

BibTex

Txt

Milestone

Received: 1900-01-01
Revised: 1900-01-01

Article Metric

Article Views(1932)
PDF Downloads(281)
Cited by(0)

Policy on re-use

To reuse of subscription content published by CPC, the users need to request permission from CPC, unless the content was published under an Open Access license which automatically permits that type of reuse.

通讯作者: 陈斌, bchen63@163.com

1.
沈阳化工大学材料科学与工程学院沈阳 110142

THE GEOMETRIC MEANING OF THE RICCATI EQUATION RELATED TO SINE-GORDON EQUATION

WU Yong-Shi ^,
GE Mo-Lin

Corresponding author: WU Yong-Shi,

Received Date: 1900-01-01
Accepted Date: 1900-01-01
Available Online: 1983-10-05

Abstract: The geometric meaning of the Riccati equation related to the structure of space is discussed. It is shown that the Riccati equation satisfied by the stereographic projection is essentially the structure equation of space.