Numerical Inverse Scattering for the Toda Lattice

被引：11
|
作者：
Bilman, Deniz [1 ]
Trogdon, Thomas [2 ]
机构：
[1] Univ Michigan, Dept Math, 530 Church St, Ann Arbor, MI 48109 USA
[2] Univ Calif Irvine, Rowland Hall, Irvine, CA 92697 USA
来源：
COMMUNICATIONS IN MATHEMATICAL PHYSICS | 2017年 / 352卷 / 02期
基金：
美国国家科学基金会;
关键词：
RIEMANN-HILBERT PROBLEMS; LONG-TIME ASYMPTOTICS; STEEPEST DESCENT; BEHAVIOR;
D O I：
10.1007/s00220-016-2819-0
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
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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页码：805 / 879
页数：75
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