Numerical Inverse Scattering for the Toda Lattice

2015/08/07 by Bilman, Deniz, Trogdon, Thomas · 2 citations
#35Q15 #37K10 #65E05 #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1508.01788

Abstract

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 \mathcal 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.

Cited by

• Efficient computation of soliton gas primitive potentials
• Numerical inverse scattering transform for the coupled modified Korteweg-de Vries equation

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