相关论文: Plane wave stability of some conservative schemes …
Plane wave solutions to the cubic nonlinear Schr\"odinger equation on a torus have recently been shown to behave orbitally stable. Under generic perturbations of the initial data that are small in a high-order Sobolev norm, plane waves are…
We study the existence and stability of periodic traveling-wave solutions for the quadratic and cubic nonlinear Schr\"odinger equations in one space dimension.
We investigate the stability of plane wave solutions of equations describing quantum particles interacting with a complex environment. The models take the form of PDE systems with a non local (in space or in space and time) self-consistent…
It is shown that plane wave solutions to the cubic nonlinear Schr\"odinger equation on a torus behave orbitally stable under generic perturbations of the initial data that are small in a high-order Sobolev norm, over long times that extend…
The present contribution contains a quite extensive theory for the stability analysis of plane periodic waves of general Schr{\"o}dinger equations. On one hand, we put the one-dimensional theory, or in other words the stability theory for…
Via minimization arguments and Concentration Compactness Principle, we prove the orbital stability of standing wave solutions for a class of quasilinear Schr\"{o}dinger equation arising from physics.
We investigate the stability and long-term behavior of spatially periodic plane waves in the complex Klein-Gordon equation under localized perturbations. Such perturbations render the wave neither localized nor periodic, placing its…
We study a system of nonlinear Schr\"odinger equations with cubic interactions in one space dimension. The orbital stability and instability of semitrivial standing wave solutions are studied for both non-degenerate and degenerate cases.
We show the existence of ground state and orbital stability of standing waves of fractional Schr\"{o}dinger equations with power type nonlinearity. For this purpose we establish the uniqueness of weak solutions.
In this paper we establish the orbital stability of standing wave solutions associated to the one-dimensional Schr\"odinger-Kirchhoff equation. The presence of a mixed term gives us more dispersion, and consequently, a different scenario…
In this paper, we prove existence and orbital stability results of periodic standing waves for the cubic-quintic nonlinear Schr\"odinger equation. We use the implicit function theorem to construct a smooth curve of explicit periodic waves…
The cubic nonlinear Schr\"odinger equation with repulsive nonlinearity and an elliptic function potential models a quasi-one-dimensional repulsive dilute gas Bose-Einstein condensate trapped in a standing light wave. New families of…
In this paper, kinds of Schr\"{o}dinger type equations with slowly decaying linear potential and power type or convolution type nonlinearities are considered. By using the concentration compactness principle, the sharp Gagliardo-Nirenberg…
Considered in this report is the one-dimensional fourth-order dispersive cubic nonlinear Schr\"odinger equation with mixed dispersion. Orbital stability, in the energy space, of a particular standing-wave solution is proved in the context…
Orbital stability property for weakly coupled nonlinear Schr\"odinger equations is investigated. Different families of orbitally stable standing waves solutions will be found, generated by different classes of solutions of the associated…
In this paper, we determine the spectral instability of periodic odd waves for the defocusing fractional cubic nonlinear Schr\"odinger equation. Our approach is based on periodic perturbations that have the same period as the standing wave…
We study the stability of the cnoidal, dnoidal and snoidal elliptic functions as spatially-periodic standing wave solutions of the 1D cubic nonlinear Schr{\"o}dinger equations. First, we give global variational characterizations of each of…
In this article, we first employ the concentration compactness techniques to prove existence and stability results of standing waves for nonlinear fractional Schr\"{o}dinger-Choquard equation \[ i\partial_t\Psi + (-\Delta)^{\alpha}\Psi = a…
We consider the focusing energy-critical Schr{\"o}dinger equation on the Heisenberg group in the radial case\[i\partial_t u-\Delta_{\mathbb{H}^1}…
We prove the orbital stability of periodic traveling-wave solutions for systems of dispersive equations with coupled nonlinear terms. Our method is basically developed under two assumptions: one concerning the spectrum of the linearized…