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Adiabatic Midpoint Rule for the dispersion-managed nonlinear Schrödinger Equation

Jahnke, Tobias; Mikl, Marcel

Abstract:
The dispersion-managed nonlinear Schrödinger equation contains a rapidly changing discontinuous coefficient function. Approximating the solution numerically is a challenging task because typical solutions oscillate in time which imposes severe step-size restrictions for traditional methods. We present and analyze a tailor-made time integrator which attains the desired accuracy with a significantly larger step-size than traditional methods. The construction of this method is based on a favorable transformation to an equivalent problem and the explicit computation of certain integrals over highly oscillatory phases. The error analysis requires the thorough investigation of various cancellation effects which result in improved accuracy for special step-sizes.


Zugehörige Institution(en) am KIT Institut für Angewandte und Numerische Mathematik (IANM)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht
Jahr 2016
Sprache Englisch
Identifikator DOI(KIT): 10.5445/IR/1000060572
ISSN: 2365-662X
URN: urn:nbn:de:swb:90-605728
KITopen ID: 1000060572
Verlag KIT, Karlsruhe
Umfang 31 S.
Serie CRC 1173 ; 2016/28
Schlagworte dispersion management, nonlinear Schrödinger equation, highly oscillatory problem, discontinuous coefficients, adiabatic integrator, error bounds, limit dynamics
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