Related papers: Standing Waves for Schr\"{o}dinger Equations with …
We present trapped solitary wave solutions of a coupled nonlinear Schr\"odinger system in $1$+$1$ dimensions in the presence of an external, supersymmetric and complex $\mathcal{PT}$-symmetric potential. The Schr\"odinger system this work…
A nonlinear Schr\"odinger equation with variable coefficients for surface waves on a large-scale steady nonuniform current has been derived without the assumption of a relative smallness of the velocity of the current. This equation can…
We study existence and stability properties of ground-state standing waves for two-dimensional nonlinear Schr\"odinger equation with a point interaction and a focusing power nonlinearity. The Schr\"odinger operator with a point interaction…
For a nonlinear Schr\"odinger system with mass critical exponent, we prove the existence and orbital stability of standing-wave solutions obtained as minimizers of the underlying energy functional restricted to a double mass constraint. In…
We consider the one-dimensional logarithmic Schr\"odinger equation with a delta potential. Global well-posedness is verified for the Cauchy problem in H1(R) and in an appropriate Orlicz space. In the attractive case, we prove orbital…
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…
This manuscript investigates the existence and spectral stability of multiple periodic standing wave solutions for a nonlinear Schr\"odinger system. By considering both cnoidal and snoidal profiles, we provide a comprehensive spectral…
We are concerned with the solvability of linear second order elliptic partial differential equations with nonlinear boundary conditions at resonance, in which the nonlinear boundary conditions perturbation is not necessarily required to…
In this paper we study the existence and the instability of standing waves with prescribed $L^2$-norm for a class of Schr\"odinger-Poisson-Slater equations in $\R^{3}$ %orbitally stable standing waves with arbitray charge for the following…
The existence of nonzero periodic travelling wave solutions for a general discrete nonlinear Schr\"odinger equation (DNLS) on finite one-dimensional lattices is proved. The DNLS features a general nonlinear term and variable range of…
We study standing waves for a system of nonlinear Schr\"odinger equations with three waves interaction arising as a model for the Raman amplification in a plasma. We consider the mass-critical and mass-supercritical regimes, and we prove…
We look for traveling wave solutions to the nonlinear Schr\"odinger equation with a subsonic speed, covering several physical models with Sobolev subcritical nonlinear effects. Our approach is based on a variant of Sobolev-type inequality…
In this paper we establish existence and stability results concerning fully nontrivial solitary-wave solutions to 3-coupled nonlinear Schr\"odinger system \[ i\partial_t u_{j}+\partial_{xx}u_{j}+ \left(\sum_{k=1}^{3} a_{kj}…
We study the concentrated NLS on ${\mathbf R^n}$, with power non-linearities, driven by the fractional Laplacian, $(-\Delta)^s, s>\frac{n}{2}$. We construct the solitary waves explicitly, in an optimal range of the parameters, so that they…
We begin to study in this paper orbital and asymptotic stability of standing waves for a model of Schr\"odinger equation with concentrated nonlinearity in dimension three. The nonlinearity is obtained considering a {point} (or contact)…
We introduce a novel framework for the analysis of linear wave equations on nonstationary asymptotically flat spacetimes, under the assumptions of mode stability and absence of zero energy resonances for a stationary model operator. Our…
We prove strong instability (instability by blowup) of standing waves for some nonlinear Schr\"odinger equations with double power nonlinearity.
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…
We study the orbital stablity and instability of solitary wave solutions for nonlinear Schr\"odinger equations of derivative type.
Under investigation in this work is an extended nonlinear Schr\"{o}dinger equation with nonzero boundary conditions, which can model the propagation of waves in dispersive media. Firstly, a matrix Riemann-Hilbert problem for the equation…