Related papers: Multiple normalized standing-waves solutions to th…
Existence results for radially symmetric oscillating solutions for a class of nonlinear autonomous Helmholtz equations are given and their exact asymptotic behavior at infinity is established. Some generalizations to nonautonomous radial…
From the work on the weak-null condition by Lindblad and Rodnianski, it is well-known that `bad' quadratic sourcing terms are allowed to appear in coupled semilinear wave equations in three spatial dimensions, provided that such terms…
We study the existence and stability of standing waves solutions of a three-coupled nonlinear Schr\"{o}dinger system related to the Raman amplification in a plasma. By means of the concentration-compacteness method, we provide a…
In this paper we consider the logarithmic Schr\"{o}dinger equation on a star graph. By using a compactness method, we construct a unique global solution of the associated Cauchy problem in a suitable functional framework. Then we show the…
We consider a nonlinear Klein Gordon equation (NLKG) with short range potential with eigenvalues and show that in the contest of complex valued solutions the small standing waves are attractors for small solutions of the NLKG. This extends…
We give a new method to prove the existence, non-existence, multiplicity, orbital stability/instability of standing waves for NLS with partial confinement without the subcritical hypothesis, even in the reduction equation. Using this…
We study standing waves for the nonlinear Schr\"odinger equation on a discrete graph. We characterize for a self-adjoint realizations of Schr\"odinger operators conditions related with the geometry of the graph that guarantee discreteness…
For a damped wave (or Klein-Gordon) equation on a bounded domain, with a focusing power-like nonlinearity satisfying some growth conditions, we prove that a global solution is bounded in the energy space, uniformly in time. Our result…
In the present work, we consider the existence and spectral stability of standing wave solutions to a model for light propagation in a twisted multi-core fiber with no gain or loss of energy. Numerical parameter continuation experiments…
In this paper we show that the hydrodynamic problem for three-dimensional water waves with strong surface-tension effects admits a fully localised solitary wave which decays to the undisturbed state of the water in every horizontal…
In this paper, we study the existence of ground state standing waves and orbital stability, of prescribed mass, for the nonlinear critical Choquard equation \begin{equation*} \left\{\begin{array}{l} i \partial_t u+\Delta u…
In this paper we consider the Klein-Gordon-Maxwell system in the electrostatic case, assuming the fall-off large-distance requirement on the gauge potential. We are interested in proving the existence of finite energy (and finite charge)…
In this paper we look for standing waves for nonlinear Schr\"odinger equations $$ i\frac{\partial \psi}{\partial t}+\Delta \psi - g(|y|) \psi -W^{\prime}(| \psi |)\frac{\psi}{| \psi |}=0 $$ with cylindrically symmetric potentials $g$…
We prove an asymptotic stability result for the water wave equations linearized around small solitary waves. The equations we consider govern irrotational flow of a fluid with constant density bounded below by a rigid horizontal bottom and…
We study the instability of standing wave solutions for nonlinear Schr\"{o}dinger equations with a one-dimensional harmonic potential in dimension $N\ge 2$. We prove that if the nonlinearity is $L^2$-critical or supercritical in dimension…
We present an existence and stability theory for gravity-capillary solitary waves with constant vorticity on the surface of a body of water of finite depth. Exploiting a rotational version of the classical variational principle, we prove…
We study the stability of standing wave solutions to a one-dimensional Gross-Pitaevsky equation with a periodic potential. We use some simple complex analysis and the Hamiltonian structure of the problem to give a simple rigorous criterion…
We prove the existence of small steady periodic capillary-gravity water waves for general stratified flows, where we allow for stagnation points in the flow. We establish the existence of both laminar and non-laminar flow solutions for the…
We prove the asymptotic stability of the moving kinks for the nonlinear relativistic wave equations in one space dimension with a Ginzburg-Landau potential: starting in a small neighborhood of the kink, the solution, asymptotically in time,…
We study the stability of the standing wave solutions of a Gross-Pitaevskii equation describing Bose-Einstein condensation of dipolar quantum gases and characterize their orbit. As an intermediate step, we consider the corresponding…