2-D Shapes Are Behind the Drapes! by Tracy Kompelien

By Tracy Kompelien

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Title: 2-D Shapes Are in the back of the Drapes!
Author: Kompelien, Tracy
Publisher: Abdo Group
Publication Date: 2006/09/01
Number of Pages: 24
Binding style: LIBRARY
Library of Congress: 2006012570

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Springer-Verlag, Berlin, 1977. 168. J. Corones, B. L. Markovski, and V. A. Rizov. A Lie group framework for soliton equations. I. Path independent case. J. Math. , 18:2207, 1977. 169. A. Lichnerowicz. Les varietes de Poisson et leurs algebres de Lie associees. J. Diff. , 12(2):253–300, 1977. 170. S. Helgason. Differential Geometry, Lie Groups, and Symmetric Spaces. American Mathematical Society, New York, 2001. 171. A. T. Fomenko. Symplectic Geometry. Advanced Studies in Contemporary Mathematics.

Birkh¨ auser, Basel, 1987. 101. B. M. Levitan. Inverse Sturm-Liouville Problems. VSP Architecture, Zeist, The Netherlands, 1987. 102. L. A. Takhtadjan. Hamiltonian systems connected with the Dirac equation. J. Sov. , 8(2):219–228, 1973. 103. D. M. Gitman and I. V. Tyutin. Quantization of Fields with Constraints. Springer Series in Nuclear and Particle Physics. Springer-Verlag, Berlin, 1990. 104. Magri, F. A geometrical approach to the nonlinear solvable equations. In: Boiti, M. , Soliani, G. ) Non-linear Evolution Equations and Dynamical Systems: Proceedings of the Meeting Held at the University of Lecce June 20–23, 1979.

It is also solvable by the ISM applied to the gauge-transformed Lax pair. In Sect. 1, we introduce the group of gauge transformations of the Lax representations. We also explain how one can take out the auxiliary gauge degrees of freedom by properly fixing up the gauge. Thus the ZS system provides us a good example of such fixing. Another important example is known as the pole gauge; the corresponding Lax operator is ˜ ψ(x, t, λ) ≡ i dψ − λS(x, t)ψ(x, t, λ) = 0 . 76) In Sect. 2, we outline how the AKNS approach should be modified in order to handle the gauge-equivalent systems.

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