A Study on Infinite Number of Integrals of Motion ClassicallyIntegrable System With Boundary (Ⅰ)

Chen Yixin; Luo Xudong

Chinese Physics C> 1998, Vol. 22> Issue(5) : 413-423

A Study on Infinite Number of Integrals of Motion ClassicallyIntegrable System With Boundary (Ⅰ)

Chen Yixin ^, ,
Luo Xudong

Zhejiang Institutte of Modern Physics and Department of Physics, Zhejiang University Hangzhou 310027

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Abstract：
By the zero curvature condition in classically integrable system, the generating funtions for integrals of motion and equations for solving K± matices are obtained in two-dimensional integrable systems on a finite intervel with independent boundary conditions on each end. Classically integrable boundary conditions will be found by solving K± matrices. In this paper, we develop a Hamiltonian method in classically integrable system with independent boundary conditions on eath end. Our result can be applied to more integrable systems than those associated with E.K. Sklyanin's approach.

References

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Binder.in Phase Transitions and Critical Phenomena Vo1.8, eds. Domb C, Lebowitz J. Academic Publisher,1983[2] Candy J. Nucl. Phys., 1989, B324:581-596; Candy J, Lewellen D. Phys. Lett., 1991, B259:274-278[3] Witten E. Phys. Rev., 1992, D46:5469-5473[4] Ghoshal S, Zamolodchikov A B. Int. J. Mod. Phys., 1994, A9:3841-3885[5] Faddeev L D, Takhtajan A B. llamiltonian Methods in the Theory of Soliton. Springer Verlag, 1987[6] Cherdnik I V. Theor. Mat. Fiz., 1984. 61:977-983[7] Sklyanin E K. Funct. Anal. Appl., 1987, 21:164-166; J. Phys., 1988, A21:2375-2389[8] Bowcock P, Corrigan E, Dorey P E, Rie哟k R H Nucl. Phys., 1995, B445:469-500

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Chen Yixin and Luo Xudong. A Study on Infinite Number of Integrals of Motion ClassicallyIntegrable System With Boundary (Ⅰ)[J]. Chinese Physics C, 1998, 22(5): 413-423.

Chen Yixin and Luo Xudong. A Study on Infinite Number of Integrals of Motion ClassicallyIntegrable System With Boundary (Ⅰ)[J]. Chinese Physics C, 1998, 22(5): 413-423. shu

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

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沈阳化工大学材料科学与工程学院沈阳 110142

A Study on Infinite Number of Integrals of Motion ClassicallyIntegrable System With Boundary (Ⅰ)

Chen Yixin ^,
Luo Xudong

Corresponding author: Chen Yixin,

Zhejiang Institutte of Modern Physics and Department of Physics, Zhejiang University Hangzhou 310027

Received Date: 1900-01-01
Accepted Date: 1900-01-01
Available Online: 1998-05-05

Abstract: By the zero curvature condition in classically integrable system, the generating funtions for integrals of motion and equations for solving K± matices are obtained in two-dimensional integrable systems on a finite intervel with independent boundary conditions on each end. Classically integrable boundary conditions will be found by solving K± matrices. In this paper, we develop a Hamiltonian method in classically integrable system with independent boundary conditions on eath end. Our result can be applied to more integrable systems than those associated with E.K. Sklyanin's approach.