Related papers: Partially concentrating standing waves for weakly …
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 consider the one-dimensional nonlinear Schr\"odinger equation with an attractive delta potential and mass-supercritical nonlinearity. This equation admits a one-parameter family of solitary wave solutions in both the focusing and…
The tadpole graph consists of a circle and a half-line attached at a vertex. We analyze standing waves of the nonlinear Schr\"{o}dinger equation with quintic power nonlinearity equipped with the Neumann-Kirchhoff boundary conditions at the…
We study a boundary value problem related to the search of standing waves for the nonlinear Schr\"odinger equation (NLS) on graphs. Precisely we are interested in characterizing the standing waves of NLS posed on the {\it double-bridge…
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 present a new family of stationary solutions to the cubic nonlinear Schroedinger equation with a Jacobian elliptic function potential. In the limit of a sinusoidal potential our solutions model a dilute gas Bose-Einstein condensate…
We investigate standing waves with prescribed mass for a class of Schrodinger equations with competing Van Der Waals type potentials, arising in a model of non-relativistic bosonic atoms and molecules. By developing an approach based on a…
In this note we study analytically and numerically the existence and stability of standing waves for one dimensional nonlinear Schr\"odinger equations whose nonlinearities are the sum of three powers. Special attention is paid to the curves…
Consider the focussing cubic nonlinear Schr\"odinger equation in $R^3$: $$ i\psi_t+\Delta\psi = -|\psi|^2 \psi. $$ It admits special solutions of the form $e^{it\alpha}\phi$, where $\phi$ is a Schwartz function and a positive ($\phi>0$)…
We construct space quasi-periodic standing wave solutions to the nonlinear Schr\"odinger equations on R^d for arbitrary d. This is a type of quasi-periodic nonlinear Bloch-Floquet waves.
We consider the quadratic nonlinear Schr\"{o}dinger system (NLS system) \begin{align*}\begin{cases} i\partial_t u + \Delta u = v \overline{u}, \\ i\partial_t v+\kappa \Delta v = u^2, \end{cases} \text{ on } I \times \mathbb{R}^5,…
The paper discusses nonlinear singular perturbations of delta type of the fractional Schr\"odinger equation $\imath\partial_t\psi=\left(-\triangle\right)^s\psi$, with $s\in(\frac{1}{2},1]$, in dimension one. Precisely, we investigate local…
We study the nonlinear Schr\"odinger equation arising in dipolar Bose-Einstein condensate in the unstable regime. Two cases are studied: the first when the system is free, the second when gradually a trapping potential is added. In both…
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}…
The semi-classical regime of standing wave solutions of a Schr\"odinger equation in presence of non-constant electric and magnetic potentials is studied in the case of non-local nonlinearities of Hartree type. It is show that there exists a…
We are concerned with the following Schr\"odinger-Poisson equation with critical nonlinearity: \[\left\{\begin{gathered} - {\varepsilon ^2}\Delta u + V(x)u + \psi u = \lambda |u{|^{p - 2}}u + |u{|^4}u{\text{in}}{\mathbb{R}^3}, \hfill -…
In this paper, we establish the existence of ground state solutions for a fractional Schr\"odinger equation in the presence of a harmonic trapping potential. We also address the orbital stability of standing waves. Additionally, we provide…
We study the weakly coupled nonlinear Schr\"odinger system \begin{equation*} \begin{cases} -\Delta u_1 = \mu_1 u_1^{p} +\beta u_1^{\frac{p-1}{2}} u_2^{\frac{p+1}{2}}\text{ in } \Omega,\\ -\Delta u_2 = \mu_2 u_2^{p} +\beta…
In this paper we study the existence and stability of normalized standing waves for the nonlinear Schr\"odinger equation on a general starlike graph with potentials. Under general assumptions on the graph and the potential, we show the…
In this paper, we study the solitary wave and the Cauchy problem for Half-wave-Schr\"{o}dinger equations in the plane. First, we show the existence and orbital stability of the ground states. Secondly, we prove that traveling waves exist…