Numerical Inverse Scattering for the Toda Lattice

We present a method to compute the inverse scattering transform (IST) for the famed Toda lattice by solving the associated Riemann–Hilbert (RH) problem numerically. Deformations for the RH problem are incorporated so that the IST can be evaluated in O ( 1 ) operations for arbitrary points in the ( n...

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Bibliographic Details
Published in:Communications in mathematical physics 2017-06, Vol.352 (2), p.805-879
Main Authors: Bilman, Deniz, Trogdon, Thomas
Format: Article
Language:English
Subjects:
Classical and Quantum Gravitation
Complex Systems
Inverse scattering
Mathematical and Computational Physics
Mathematical Physics
Physics
Physics and Astronomy
Quantum Physics
Relativity Theory
Theoretical
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Summary:We present a method to compute the inverse scattering transform (IST) for the famed Toda lattice by solving the associated Riemann–Hilbert (RH) problem numerically. Deformations for the RH problem are incorporated so that the IST can be evaluated in O ( 1 ) operations for arbitrary points in the ( n, t )-domain, including short- and long-time regimes. No time-stepping is required to compute the solution because ( n, t ) appear as parameters in the associated RH problem. The solution of the Toda lattice is computed in long-time asymptotic regions where the asymptotics are not known rigorously.
ISSN:0010-3616
1432-0916
DOI:10.1007/s00220-016-2819-0