Journal
COMMUNICATIONS IN MATHEMATICAL PHYSICS
Volume 352, Issue 2, Pages 805-879Publisher
SPRINGER
DOI: 10.1007/s00220-016-2819-0
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Funding
- National Science Foundation through the NSF [DMS-1150427, DMS-1303018]
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1150427] Funding Source: National Science Foundation
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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 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.
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