【摘 要】
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Polynomials of confocal type appeared first in the classical integrable systems,such as the Jacobis geodesic flow on ellipsoid and the C Neumanns system,describ
【机 构】
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DepartmentofMathematics,ZhengzhouUniversity,China
【出 处】
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International Conference on Orthogonal Polynomials,Integrabl
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Polynomials of confocal type appeared first in the classical integrable systems,such as the Jacobis geodesic flow on ellipsoid and the C Neumanns system,describing the harmonic oscillation of particles constrained on sphere.They are successfully used by J.Moser in calculating the finite-band solution of the KdV equation.In this talk,confocal polynomials associated with the ZS-AKNS spectral problem are constructed.They support the Liouville integrability of some Hamiltonian systems and symplectic maps,which are applied to calculate explicit analytic solutions of some soliton equations,including the discrete nonlinear Schr(¨o)dinger equation and the discrete Kadomtsev-Petviashvilli equation.
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