Bifurcation from semi-trivial standing waves and ground states for a system of nonlinear Schrödinger equations

Details Bifurcation from semi-trivial standing waves and ground states for a system of nonlinear Schrödinger equations Bifurcation from semi-trivial standing waves and ground states for a system of nonlinear Schrödinger equations

2011-02-08

arxiv.org/abs/1102.1545v1

Mathematics

Analysis of PDEs

25 pages, 2 figures

Scientific paper

We consider a system of nonlinear Schr\"{o}dinger equations related to the Raman amplification in a plasma. We study the orbital stability and instability of standing waves bifurcating from the semi-trivial standing wave of the system. The stability and instability of the semi-trivial standing wave at the bifurcation point are also studied. Moreover, we determine the set of the ground states completely.

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