NLS approximation of time oscillatory long waves for equations with quasilinear quadratic terms | Zendy

ChirilusBruckner Martina | Zendy; Düll WolfPatrick | Zendy; Schneider Guido | Zendy

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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.

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