Diffractive Nonlinear Geometric Optics for Short Pulses
نویسندگان
چکیده
منابع مشابه
Diffractive Nonlinear Geometric Optics for Short Pulses
This paper considers the behavior of pulse-like solutions of length ε 1 to semilinear systems of hyperbolic partial differential equations on the time scale t = O(1/ε) of diffractive geometric optics. The amplitude is chosen so that nonlinear effects influence the leading term in the asymptotics. For pulses of larger amplitude so that the nonlinear effects are pertinent for times t = O(1), accu...
متن کاملDiffractive Nonlinear Geometric Optics *
Contents. x1. The origin and nature of Schrr odinger type approximations. x2. Formulating the ansatz. x3. Equations for the prooles. x4. Solvability of the the proole equations. x5. Convergence towards exact solutions. x6. The quasilinear case.
متن کاملDiffractive Nonlinear Geometric Optics with Rectification
This paper studies high frequency solutions of nonlinear hyperbolic equations for time scales at which diiractive eeects and nonlinear eeects are both present in the leading term of approximate solutions. The key innovation is the analysis of rectiication eeects, that is the interaction of the nonoscillatory local mean eld with the rapidly oscillating elds. The main results prove that in the li...
متن کاملAmplification of pulses in nonlinear geometric optics
In this companion paper to our study of amplification of wavetrains [CGW13], we study weakly stable semilinear hyperbolic boundary value problems with pulse data. Here weak stability means that exponentially growing modes are absent, but the so-called uniform Lopatinskii condition fails at some boundary frequency in the hyperbolic region. As a consequence of this degeneracy there is again an am...
متن کاملNonlinear geometric optics for reflecting uniformly stable pulses
We provide a justification with rigorous error estimates showing that the leading term in weakly nonlinear geometric optics expansions of highly oscillatory reflecting pulses is close to the uniquely determined exact solution for small wavelengths ε. Pulses reflecting off fixed noncharacteristic boundaries are considered under the assumption that the underlying boundary problem is uniformly spe...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: SIAM Journal on Mathematical Analysis
سال: 2003
ISSN: 0036-1410,1095-7154
DOI: 10.1137/s0036141002403584