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

Abstract

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 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.

25 pages, 2 figures

References in corpus (1)

• Instability of bound states for abstract nonlinear Schrödinger equations

Cited by in corpus (2)

• Well-posedness and scattering for a system of quadratic derivative nonlinear Schrödinger equations with low regularity initial data
• Instability of bound states for abstract nonlinear Schrödinger equations