Abstract
By using a general scheme for decomposing a zero-curvature equation into two commutingx- andt n -finite-dimensional integrable Hamiltonian systems (FDIHS), a systematic deduction of the Lax representation for all constrained flows of the AKNS hierarchy from the adjoint representation of the two auxiliary linear problems is presented. The Darboux transformation for these FDIHSs is derived.
Similar content being viewed by others
References
Cao Cewen, A cubic system which generates Bargmann potential andN-gap solutions,Chinese Quarterly J of Math, 1988,3: 90–96.
Zeng Yunbo, Li Yishen, The constraints of potentials and the finite-dimensional integrable systems,J Math Phys, 1989,30: 1679–1689.
Zeng Yunbo, Li Yishen, An approach to the integrability of the Hamiltonian systems obtained by reduction,J Phys A, 1990,23: L89-L94.
Zeng Yunbo, An approach to the deduction of the finite-dimensional integrability from the infinite-dimensional integrability,Phys Lett A, 1991,160: 541–547.
Zeng Yunbo, Li Yishen, On a general approach from infinite-dimensional integrable Hamiltonian systems to finite-dimensional ones,Advances in Math, 1995,24: 112–130.
Zeng Yunbo, Li Yishen, The deduction of the Lax representation for constrained flows from the adjoint representation,J Phys A, 1993,26: L273-L278.
Ablowitz M J, Segur H,Solitons and Inverse Scattering Transformation, Philadelpia: SIAM, 1981.
Newell A C,Solitons in Mathematics and Physics, Philadelphia: SIAM, 1985.
Tu Guizhang, The trace identity, a powerful tool for constructing the Hamiltonian structure of integrable system,J Math Phys, 1989,30: 330–338.
Faddeev L D, Takhtajan L A,Hamiltonian Methods in the Theory of Solitons, Heidelberg: Spriger, 1987.
Deleón M, Rodrigues P R,Generalized Classical Mechanics and Field Theory, North-Holland, Amsterdam, 1985.
Li Yishen, Gu Xinshen, Zou Maorong, Three kinds of Darboux transformations for the evolution equations which connect with AKNS eigenvalue problem,Acta Math Sinica, 1987,3: 143–151.
Gu Chaohao, Zhou Zixiang, On the Darboux matrices of Backlund transformation for the AKNS system,Lett Math Phys, 1987,12: 169.
Author information
Authors and Affiliations
Additional information
Supported by the Chinese National Basic Research Project “Nonlinear Science”
Rights and permissions
About this article
Cite this article
Yunbo, Z., Yishen, L. The Lax representation and Darboux transformation for constrained flows of the AKNS hierarchy. Acta Mathematica Sinica 12, 217–224 (1996). https://doi.org/10.1007/BF02108164
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02108164