Bifurcation from Semitrivial Standing Waves and Ground States for a System of Nonlinear Schrödinger Equations

We consider a system of nonlinear Schrödinger equations related to the Raman amplification in a plasma. We study the orbital stability and instability of standing waves bifurcating from the semitrivial standing wave of the system. The stability and instability of the semitrivial standing wave at the...

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Bibliographic Details
Published in:SIAM journal on mathematical analysis 2012-01, Vol.44 (1), p.206-223
Main Authors: Colin, Mathieu, Ohta, Masahito
Format: Article
Language:English
Subjects:
Electrons
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Summary:We consider a system of nonlinear Schrödinger equations related to the Raman amplification in a plasma. We study the orbital stability and instability of standing waves bifurcating from the semitrivial standing wave of the system. The stability and instability of the semitrivial standing wave at the bifurcation point are also studied. Moreover, we determine the set of the ground states completely.
ISSN:0036-1410
1095-7154
DOI:10.1137/110823808