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NLS approximation of time oscillatory long waves for equations with quasilinear quadratic terms
Author(s) -
ChirilusBruckner Martina,
Düll WolfPatrick,
Schneider Guido
Publication year - 2015
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201200325
Subject(s) - quadratic equation , mathematics , nonlinear system , mathematical analysis , envelope (radar) , wave equation , physics , quantum mechanics , geometry , telecommunications , radar , computer science
We consider a nonlinear wave equation with a quasilinear quadratic nonlinearity. Slow spatial and temporal modulations of the envelope of an underlying carrier wave e i ( k 0 x − ω 0 t )can be described formally by an NLS equation. It is the purpose of this paper to present a method which allows to prove error estimates between this formal approximation and true solutions of the quasilinear wave equation in casek 0 = 0 . The paper contains the first validity proof of the NLS approximation for a nonlinear wave equation with quasilinear quadratic terms.