On the long time behavior of the doubly infinite toda lattice under initial data decaying at infinity
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We provide rigorous analysis of the long time behavior of the (doubly infinite) Toda lattice under initial data that decay at infinity, in the absence of solitions. We solve (approximately and for large times) the Riemann-Hilbert matrix factorization problem equivalent to the related inverse scattering problem with the help of the Beals-Coifman formula, by reducing it to a simpler one through a series of contour deformations in the spirit of the Deift-Zhou method.
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