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.

引用

页码：805 / 879

页数：75

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