Abstract
The parametric representation for finite-band solutions of a stationary soliton equation is discussed. This parametric representation can be represented as a Hamiltonian system which is integrable in Liouville sense. The nonconfocal involutive integral representations {F m } are obtained also. The finite-band solutions of the soliton equation can be represented as the solutions of two set of ordinary differential equations.
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C.W. Cao, X.G. Geng. A Nonconfocal Generator of Involutive Systems and three Associated Soliton Hierarchies.J. Math. Phys., 1991, 32: 2323–2327
S.M. Zhu. The Lax Representation of a Hierarchy of Solution Equation. The 2nd Asian Mathematics Conference, Thailand, 1995
O. Regnisco, C.W. Cao, Y.T. Wu. On the Relation of the Stationary Toda Equation and the Symplectic Maps.J. Phys. A: Math. Gen., 1995, 28: 573–588
C.W. Cao. Nonlinearization of the Lax System for AKNS Hierarchy.Sci. in China (Series A), 1990, 33: 528–536
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This work is supported by the National Natural Science Fundation of China (No. 10071097).
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Lei, Z., Qiyan, S. The integrability and parametric representation of a hierarchy of soliton equations. Acta Mathematicae Applicatae Sinica 17, 310–316 (2001). https://doi.org/10.1007/BF02677374
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DOI: https://doi.org/10.1007/BF02677374