Related papers: Nonlinear Schr\"odinger equation with bounded magn…
We propose an approach that permits to avoid instability phenomena for the nonlinear Schrodinger equations. We show that by approximating the solution in a suitable way, relying on a frequency cut-off, global well-posedness is obtained in…
For the first time, the general nonlinear Schr\"odinger equation is investigated, in which the chromatic dispersion and potential are specified by two arbitrary functions. The equation in question is a natural generalization of a wide class…
We investigate existence and qualitative behaviour of solutions to nonlinear Schr\"odinger equations with critical exponent and singular electromagnetic potentials. We are concerned with magnetic vector potentials which are homogeneous of…
An explicit two-soliton solution for the derivative nonlinear Schr\"odinger equation with nonvanishing boundary conditions is derived, demonstrating details of interactions between two bright solitons, two dark solitons, as well as one…
We consider the semi-classical limit of nonlinear Schrodinger equations in the presence of both a polynomial nonlinearity and thederivative in space of a polynomial nonlinearity. By working in a class of analytic initial data, we do not…
We show that the two-dimensional, nonlinear Schr\"odinger lattice with a saturable nonlinearity admits periodic and pulse-like exact solutions. We establish the general formalism for the stability considerations of these solutions and give…
In this paper we prove global existence and uniqueness of solutions to the stochastic logarithmic Schr\"odinger equation with linear multiplicative noise. Our approach is mainly based on the rescaling approach and the method of maximal…
We establish the second quantized solution of the nonlinear Schrodinger equation on the half line with a mixed boundary condition. The solution is based on a new algebraic structure, which we call boundary exchange algebra and which…
In this study, we consider two nonlinear Schr\"{o}dinger-type models that are derived by R L. Frank, F. M\'{e}hats, C. Sparber [arXiv:1611.01574] to study 3D nonlinear Schr\"{o}dinger equations under strong magnetic fields. One model is…
In this paper we prove the existence of a nontrivial solution to the nonlinear Schrodinger-Maxwell equations in $\R^3,$ assuming on the nonlinearity the general hypotheses introduced by Berestycki & Lions.
In this paper we investigate the existence of positive solutions and ground state solution for a class of fractional Schr\"odinger-Poisson equations in $\mathbb R^3$ with general nonlinearities.
An explicit lifespan estimate is presented for the derivative Schr\"odinger equations with periodic boundary condition.
The goal is a construction of stationary solutions close to a non-trivial combination of two plane waves at high energies for a periodic non-linear Schroedinger equation in dimension two. The corresponding isoenergetic surfaces are…
We consider the one-dimensional nonlinear Schr\"odinger equation with Dirichlet boundary conditions in the fully resonant case (absence of the zero-mass term). We investigate conservation of small amplitude periodic-solutions for a large…
We analize the Nonlinear Schr\"odinger Equation.
We investigate the existence of solutions to the fractional nonlinear Schr\"{o}dinger equation $(-\Delta)^s u = f(u)$ with prescribed $L^2$-norm $\int_{\mathbb{R}^N} |u|^2 \, dx =m$ in the Sobolev space $H^s(\mathbb{R}^N)$. Under fairly…
We discuss the global existence of solutions to a system of stochastic Schr\"odinger equations with multiplicative noise. Our setting of the quadratic nonlinear terms in dimension 4 is $L^2$-critical. We treat the solutions under the ground…
We study the Derivative Nonlinear Schr\"odinger equation for general initial conditions in weighted Sobolev spaces that can support bright solitons (but excluding spectral singularities). We prove global well-posedness and give a full…
This work studies the initial-boundary value problem for both the linear Schr\"odinger equation and the cubic nonlinear Schr\"odinger equation on the half-space in higher dimensions ($n\ge 2$). First, the forced linear problem is solved on…
We consider some nonlinear fractional Schr\"odinger equations with magnetic field and involving continuous nonlinearities having subcritical, critical or supercritical growth. Under a local condition on the potential, we use minimax methods…