相关论文: Coordinates at small energy and refined profiles f…
In this note, we give an alternative proof of the theorem on soliton selection for small energy solutions of nonlinear Schr\"odinger equations (NLS) which we studied in Anal. PDE 8 (2015), 1289-1349 and more recently in Annals of PDE (2021)…
In this paper, we give an alternative proof for the asymptotic stability of solitons for nonlinear Schr\"odinger equations with internal modes. The novel idea is to use "refined profiles" developed by the authors for the analysis of small…
We study the quasi-periodic standing wave solutions of the focusing and defocusing cubic nonlinear Schr{\"o}dinger equations in dimension one. In the defocusing case, we establish a diffeomorphic correspondence between the invariants of the…
In this work, we investigate the existence and orbital (in)stability of several branches of standing--wave solutions for the cubic nonlinear Schr\"odinger equation (NLS) posed on a looping--edge graph $\mathcal{G}$, consisting of a circle…
We study the long time behavior of small (in $l^2$) solutions of discrete nonlinear Schr\"odinger equations with potential. In particular, we are interested in the case that the corresponding discrete Schr\"odinger operator has exactly two…
Consider a bounded solution of the focusing, energy-critical wave equation that does not scatter to a linear solution. We prove that this solution converges in some weak sense, along a sequence of times and up to scaling and space…
We consider a model equation from [14] that captures important properties of the water wave equation. We give a new proof of the fact that wave packet solutions of this equation are approximated by the nonlinear Schrodinger equation. This…
In the present paper, we construct modified wave operators for the defocusing cubic nonlinear Schr\"odinger equation (NLS) in one space dimension without size restriction on scattering data. In the proof, we introduce a new formulation of…
For the Schr\"odinger equation with a cubic-quintic, focusing-focusing nonlinearity in one space dimension, this article proves the local asymptotic completeness of the family of small standing solitary waves under even perturbations in the…
In this work, we study the existence and orbital (in)stability of certain standing-wave solutions for the cubic nonlinear Schr\"odinger equation (NLS) posed on a looping-edge graph $\mathcal{G}$, consisting of a circle and a finite number…
In this paper, we study critical semilinear nonlocal elliptic equations involving the logarithmic Schr\"odinger operator and its fractional pseudo-relativistic counterpart, both arising in quantum models with nonlocal and relativistic…
This paper completes the program started in arXiv:2104.11204 and arXiv:2110.04565 aiming at providing a full rigorous justification of the wave kinetic theory for the nonlinear Schr\"odinger (NLS) equation. Here, we cover the full range of…
In this work, we study the existence of various classes of standing waves for a nonlinear Schr\"odinger system with quadratic interaction, along with a harmonic or partially harmonic potential. We establish the existence of ground-state…
We prove that standing-waves solutions to the non-linear Schr\"odinger equation in dimension one whose profiles can be obtained as minima of the energy over the mass, are orbitally stable and non-degenerate, provided the non-linear term $ G…
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…
Using the Fermi Golden Rule analysis developed in several results by the first author, we prove asymptotic stability of asymmetric nonlinear bound states bifurcating from linear bound states for a quintic nonlinear Schr\"odinger operator…
We prove the existence of a class of orbitally stable bound state solutions to nonlinear Schr\"odinger equations with super-quadratic confinement in two and three spatial dimensions. These solutions are given by time-dependent rotations of…
We consider a non-conservative nonlinear Schrodinger equation (NCNLS) with time-dependent coefficients, inspired by a water waves problem. This problem does not have mass or energy conservation, but instead mass and energy change in time…
The present paper is the first part of a project devoted to the fractional nonlinear Schr\"{o}dinger (fNLS) equation. It is concerned with the existence and numerical generation of the solitary-wave solutions. For the first point, some…
We develop a detailed rigorous analysis of edge bifurcations of standing waves in the nonlinear Schr\"odinger (NLS) equation on a tadpole graph (a ring attached to a semi-infinite line subject to the Kirchhoff boundary conditions at the…