On numerical inverse scattering for the Korteweg-de Vries equation with discontinuous step-like data

被引:9
作者
Bilman, Deniz [1 ]
Trogdon, Thomas [2 ]
机构
[1] Univ Cincinnati, Cincinnati, OH 45221 USA
[2] Univ Washington, Seattle, WA 98195 USA
关键词
inverse scattering; step-like data; Riemann-Hilbert problems; dispersive shock waves; SMALL DISPERSION LIMIT; DEVRIES EQUATION; ASYMPTOTICS; WAVES;
D O I
10.1088/1361-6544/ab6c37
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We present a method to compute dispersive shock wave solutions of the Korteweg-de Vries equation that emerge from initial data with step-like boundary conditions at infinity. We derive two different Riemann-Hilbert problems associated with the inverse scattering transform for the classical Schrodinger operator with possibly discontinuous, step-like potentials and develop relevant theory to ensure unique solvability of these problems. We then numerically implement the Deift-Zhou method of nonlinear steepest descent to compute the solution of the Cauchy problem for small times and in two asymptotic regions. Our method applies to continuous and discontinuous initial data.
引用
收藏
页码:2211 / 2269
页数:59
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