Related papers: An instability criterion for nonlinear standing wa…
This work focuses on the study of solitary wave solutions to a nonlocal, nonlinear Schr\"odinger system in $1$+$1$ dimensions with arbitrary nonlinearity parameter $\kappa$. Although the system we study here was first reported by Yang…
This paper is motivated by a gauged Schr\"{o}dinger equation in dimension 2. We are concerned with radial stationary states under the presence of a vortex at the origin. Those states solve a nonlinear nonlocal PDE with a variational…
The parametrically driven damped nonlinear Schr\"odinger equation serves as an amplitude equation for a variety of resonantly forced oscillatory systems on the plane. In this note, we consider its nodal soliton solutions. We show that…
We study the evolution of nonlinear surface gravity water-wave packets developing from modulational instability over an uneven bottom. A nonlinear Schr\"odinger equation (NLSE) with coefficients varying in space along propagation is used as…
We consider standing waves with frequency $\omega$ for 4-superlinear Schr\"odinger-Poisson system. For large $\omega$ the problem reduces to a system of elliptic equations in $\mathsf{R}^3$ with potential indefinite in sign. The variational…
We show the existence of ground state and orbital stability of standing waves of fractional Schr\"{o}dinger equations with power type nonlinearity. For this purpose we establish the uniqueness of weak solutions.
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 demonstrate that stabilization of solitons of the multidimensional Schrodinger equation with a cubic nonlinearity may be achieved by a suitable periodic control of the nonlinear term. The effect of this control is to stabilize the…
We investigate the properties of localized waves in systems governed by nonlocal nonlinear Schrodinger type equations. We prove rigorously by bounding the Hamiltonian that nonlocality of the nonlinearity prevents collapse in, e.g.,…
The parametrically driven, damped nonlinear Schr\"odinger equation has two cn- and two dn-wave solutions. We show that one pair of the cn and dn solutions is unstable for any combination of the driver's strength, dissipation coefficient and…
In this paper we present some recent results concerning the ex- istence, the stability and the dynamics of solitons occurring in the nonlinear Schroedinger equation when the parameter h -> 0. We focus on the role played by the Energy and…
We study the nonlinear Schr\"odinger equation (NLS) on a star graph $\mathcal{G}$. At the vertex an interaction occurs described by a boundary condition of delta type with strength $\alpha\in \mathbb{R}$. We investigate an orbital…
In pattern forming systems such as Rayleigh-Benard convection or directional solidification, a large number of linearly stable, patterned steady states exist when the basic, simple steady state is unstable. Which of these steady states will…
A nonlinear stochastic differential equation with the order of nonlinearity higher than one, with several discrete and distributed delays and time varying coefficients is considered. It is shown that the sufficient conditions for…
We obtain new results on the stability of discrete dark solitons bifurcating from the anti-continuum limit of the discrete nonlinear Schrodinger equation, following the analysis of our previous paper [Physica D 212, 1-19 (2005)]. We derive…
The conditions under which stable evolution of two nonlinear interacting waves are derived within the context of nematic crystals. Two cases are considered: plane waves and solitons. In the first case, the modulation instability analysis…
We study statically homogeneous Bose-Einstein condensates with spatially inhomogeneous interactions and outline an experimental realization of compensating linear and nonlinear potentials that can yield constant-density solutions. We…
The nonlinear Schr\"odinger equation is widely used as an approximate model for the evolution in time of the water wave envelope. In the context of simulating ocean waves, initial conditions are typically generated from a measured power…
We study the two dimensional non-linear Schr\"odinger equation with two types of exponential non-linearities. It is well-known by a work of Ruf - Sani, that such models support solitary wave solutions, which are solutions of some…
Effects of nonlinear dynamics of solitary waves and wave modulations within the modular (also known as quadratically cubic) Korteweg - de Vries equation are studied analytically and numerically. Large wave events can occur in the course of…