New finite-gap solutions for the coupled Burgers equations engendered by the Neumann systems

doi:10.1088/1674-1056/19/9/090403

Abstract On the tangent bundle TS^N-1 of the unit sphere S^N-1, this paper reduces the coupled Burgers equations to two Neumann systems by using the nonlinearization of the Lax pair, whose Liouville integrability is displayed in the scheme of the r-matrix technique. Based on the Lax matrix of the Neumann systems, the Abel–Jacobi coordinates are appropriately chosen to straighten out the restricted Neumann flows on the complex torus, from which the new finite-gap solutions expressed by Riemann theta functions for the coupled Burgers equations are given in view of the Jacobi inversion.

Keywords: coupled Burgers equations Lax matrix Jacobi inversion finite-gap solutions

Received: 02 January 2010
Revised: 06 March 2010
Accepted manuscript online:

PACS:	0420J
	0290

Fund: Project supported by the Scientific Foundation of the Southeast University of China (Grant No. KJ2009359), the National Natural Science Foundation of China (Grant No. 10871182) and the U. S. Army Research Office (contract/grant number W911NF-08-1-0511) and Texas grant NHARP 2010.

Cite this article:

Chen Jin-Bing(陈金兵), Geng Xian-Guo(耿献国), and Qiao Zhi-Jun(乔志军) New finite-gap solutions for the coupled Burgers equations engendered by the Neumann systems 2010 Chin. Phys. B 19 090403

[1]	Kovalevski S 1889 Acta. Math. 12 177
[2]	Knorrer H 1980 Invent. Math. 59 119
[3]	Jacobi C 1984 Vorlesungen uber Dynamik Gesammelte Werke (Berlin: Supplementband)
[4]	Calogero F 1975 Lett. Nuovo Cimento 13 411
[5]	Moser J 1975 Adv. Math. 16 197
[6]	Moser J 1986 Integrable Hamiltonian System and Spectral Theory Proc. Symp. on Differential Geometry and Differential Equations (Beijing: Science Press) 157
[7]	Flascka H 1983 in: Non-linear Integrable System-Classical Theory and Quantum Theory, 1981 Proceedings of RIMS Symposium Kyoto, Japan (Singapore: World Scientific)
[8]	Cao C W 1990 Sci. China A bf33 528
[9]	Cao C W and Geng X G 1990 in Proc. Conf. on Nonlinear Physics Shanghai 1989, Research Reports in Physics (Berlin: Springer) 68
[10]	Cao C W, Wu Y T and Geng X G 1999 J. Math. Phys. bf40 3948
[11]	Qiao Z J 2001 Theor. Math. Phys. bf127 827
[12]	Geng X G and Cao C W 2001 Nonlinearity 14 1433
[13]	Zhou R G 1997 J. Math. Phys. bf38 2535
[14]	Chen J B and Geng X G 2006 Chin. Phys. 15 1407
[15]	Wu Y Q 2008 Acta Phys. Sin. 57 5390 (in Chinese)
[16]	Ji J, Yao Y Q, Yu J and Liu Y Q 2007 Chin. Phys. bf 16 296
[17]	Sklyanin E K 1992 Commun. Math. Phys. bf150 181
[18]	Qiao Z J and Zhou R G 1997 Phys. Lett. A bf235 35
[19]	Qiao Z J 2001 Rev. Math. Phys. bf13 545
[20]	Zhou R G 1998 J. Math. Phys. bf39 2848
[21]	Qiao Z J 2003 Commun. Math. Phys. bf239 309
[22]	Cao C W and Geng X G 1990 J. Phys. A: Math. Gen. bf23 4117
[23]	Levi D, Sym A and Wojciechowsk S 1983 J. Phys. A: Math. Gen. 16 2423
[24]	Babelon O and Viallet C M 1990 Phys. Lett. B 237 411
[25]	Qiao Z J 2002 Finite-dimensional Integrable System and Nonlinear Evolution Equations (Beijing: Chinese National Higher Education Press)
[26]	Arnold V I 1978 Mathematical Methods of Classical Mechanics (Berlin: Springer)
[27]	Zhou Z X 2002 J. Phys. Soc. Jpn. bf71 1857
[28]	Griffiths P and Harris J 1994 Principles of Algebraic Geometry (New York: Wiley)
[29]	Dickey L A 1991 Soliton Equations and Hamiltonian Systems (Singapore: World Scientific)
[30]	Hon Y C and Fan E G 2005 J. Math. Phys. bf46 032701

[1]	Completeness of the system of eigenvectors of off-diagonal operator matrices and its applications in elasticity theory Huang Jun-Jie(黄俊杰),Alatancang(阿拉坦仓), and Wang Hua(王华). Chin. Phys. B, 2010, 19(12): 120201.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

New finite-gap solutions for the coupled Burgers equations engendered by the Neumann systems

Cite this article:

Online attention