scholarly journals Existence and orbital stability of standing waves for the 1D Schrödinger-Kirchhoff equation

2021 ◽  
pp. 125098
Author(s):  
Fábio Natali ◽  
Eleomar Cardoso
Keyword(s):  
Standing Waves ◽  
Orbital Stability ◽  
Kirchhoff Equation

Orbital stability of standing waves for some nonlinear Schr�dinger equations

1982 ◽  
Vol 85 (4) ◽  
pp. 549-561 ◽  
Author(s):  
T. Cazenave ◽  
P. L. Lions
Keyword(s):  
Standing Waves ◽  
Orbital Stability

scholarly journals Orbital stability of standing waves for a class of Schrödinger equations with unbounded potential

2006 ◽  
Vol 2006 ◽  
pp. 1-7
Author(s):  
Guanggan Chen ◽  
Jian Zhang ◽  
Yunyun Wei
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Standing Waves ◽  
Variational Calculus ◽  
Orbital Stability ◽  
Nonlinear Schrodinger Equation ◽  
Schrödinger Equations ◽  
Nonlinear Schrödinger ◽  
Unbounded Potential

This paper is concerned with the nonlinear Schrödinger equation with an unbounded potential iϕt=−Δϕ+V(x)ϕ−μ|ϕ|p−1ϕ−λ|ϕ|q−1ϕ, x∈ℝN, t≥0, where μ>0, λ>0, and 1<p<q<1+4/N. The potential V(x) is bounded from below and satisfies V(x)→∞ as |x|→∞. From variational calculus and a compactness lemma, the existence of standing waves and their orbital stability are obtained.

scholarly journals Variational properties and orbital stability of standing waves for NLS equation on a star graph

2014 ◽  
Vol 257 (10) ◽  
pp. 3738-3777 ◽  
Author(s):  
Riccardo Adami ◽  
Claudio Cacciapuoti ◽  
Domenico Finco ◽  
Diego Noja
Keyword(s):  
Standing Waves ◽  
Orbital Stability ◽  
Star Graph ◽  
Nls Equation

Orbital stability of standing waves for nonlinear fractional Schrödinger equation with unbounded potential

2019 ◽  
Vol 12 (03) ◽  
pp. 1950043
Author(s):  
Xiaohua Liu
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Standing Waves ◽  
Orbital Stability ◽  
Fractional Schrödinger Equation ◽  
Unbounded Potential ◽  
Nonlinear Fractional Schrödinger Equation ◽  
The Stability ◽  
First Time ◽  
Fractional Schrodinger Equation

In this paper, the orbital stability of standing waves for nonlinear fractional Schrödinger equation is considered. By constructing the constrained functional extreme-value problem, the existence of standing waves is studied. With the help of the orbital stability theories presented by Grillakis, Shatah and Strauss, the orbital stability of standing waves is determined by the sign of a discriminant. To our knowledge, it is the first time that the abstract orbital stability theories presented by Grillakis, Shatah and Strauss are applied to study the stability of solutions for fractional evolution equation.

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.

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