APPROXIMATION OF HIGH-FREQUENCY WAVE PROPAGATION IN DISPERSIVE MEDIA

被引：1

作者：

Baumstark, Julian ^{[1
]}

Jahnke, Tobias ^{[1
]}

机构：

[1] Karlsruher Inst Technol, Inst Angew & Numer Math, Fak Math, Englerstr 2, D-76131 Karlsruhe, Germany

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2023年 / 55卷 / 02期

关键词：

high-frequency wave propagation; semilinear wave equation; diffractive geometric optics; slowly varying envelope approximation; Maxwell-Lorentz system; error bounds; NONLINEAR GEOMETRIC OPTICS; SHORT PULSES; SYSTEMS;

D O I：

10.1137/22M1474035

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider semilinear hyperbolic systems with a trilinear nonlinearity. Both the differential equation and the initial data contain the inverse of a small parameter E, and typical solutions oscillate with frequency proportional to 1/E in time and space. Moreover, solutions have to be computed on time intervals with length of 1/E in order to study nonlinear and diffractive effects. As a consequence, direct numerical simulations are extremely costly or even impossible. We propose an analytical approximation and prove that it approximates the exact solution up to an error of O(E2) over times of 1/E. This is a significant improvement over the classical nonlinear Schro"\dinger approximation, which only yields an accuracy of O(E).

引用

页码：1214 / 1245

页数：32