Orbital instability of standing waves for the quadratic–cubic Klein-Gordon–Schrödinger system

2014 ◽  
Vol 66 (4) ◽  
pp. 1341-1354 ◽  
Author(s):  
Fábio Natali ◽  
Ademir Pastor
Keyword(s):  
Standing Waves ◽  
Klein Gordon ◽  
Orbital Instability ◽  
Schrödinger System

Stable standing waves for the two-dimensional Klein–Gordon–Schrödinger system

2010 ◽  
Vol 140 (5) ◽  
pp. 1011-1039 ◽  
Author(s):  
Hiroaki Kikuchi
Keyword(s):  
General Theory ◽  
Perturbation Method ◽  
Ground State ◽  
Standing Waves ◽  
Orbital Stability ◽  
Two Dimensional ◽  
Spatial Dimensions ◽  
Klein Gordon ◽  
Linearized Operator ◽  
Schrödinger System

AbstractWe study the orbital stability of standing waves for the Klein–Gordon–Schrödinger system in two spatial dimensions. It is proved that the standing wave is stable if the frequency is sufficiently small. To prove this, we obtain the uniqueness of ground state and investigate the spectrum of the appropriate linearized operator by using the perturbation method developed by Genoud and Stuart and Lin and Wei. Then we apply to our system the general theory of Grillakis, Shatah and Strauss.

Orbital Instability of Standing Waves for the Klein-Gordon-Zakharov System

2008 ◽  
Vol 8 (2) ◽  
Author(s):  
Zaihui Gan
Keyword(s):  
Ground State ◽  
Solitary Wave Solution ◽  
Standing Waves ◽  
Variational Calculus ◽  
Invariant Sets ◽  
Zakharov System ◽  
Priori Estimates ◽  
Klein Gordon ◽  
Orbital Instability ◽  
Three Space

AbstractThis paper deals with the instability of the ground state solitary wave solution to the Klein-Gordon-Zakharov system in three space dimensions with c ≥ 1, which is a model to describe the Langmuir turbulence in plasma. First we construct a suitable constrained variational problem and obtain the existence of the standing waves with ground state by using variational calculus and scaling argument. Then by defining invariant sets and applying some priori estimates, we prove the orbital instability of the ground state in the following sense: in each neighborhood of it, there exists a solution whose energy diverges in finite or infinite time.

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