相关论文: Scale competition in nonlinear Schrodinger models
In this work we study a system of Schr\"odinger equations involving nonlinearities with quadratic growth. We establish sharp criterion concerned with the dichotomy global existence versus blow-up in finite time. Such a criterion is given in…
Winner-take-all phenomena are observed in various competitive systems. We find similar phenomena in replicator models with randomly fluctuating growth rates. The disparity between winners and losers increases indefinitely, even if all…
In this article, we study the standing-wave solutions to a class of systems of nonlinear Schr\"odinger equations. Our target is all the standard forms of the NLS systems, with two unknowns, that have a common linear part and cubic…
A nonlinear Schrodinger equation arising from light propagation down an inhomogeneous medium is considered. The inhomogeneity is reflected through a non-uniform coefficient of the non-linear term in the equation. In particular, a…
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 consider the stationary solutions for a class of Schroedinger equations with a symmetric double-well potential and a nonlinear perturbation. Here, in the semiclassical limit we prove that the reduction to a finite-mode approximation give…
The connection between domain relaxations at individual scales and the collective heterogeneous response in non-equilibrium systems is a topic of profound interest in recent times. In a model sys- tem of constantly driven oppositely charged…
We consider equations of nonlinear Schrodinger type augmented by nonlinear damping terms. We show that nonlinear damping prevents finite time blow-up in several situations, which we describe. We also prove that the presence of a quadratic…
All stationary solutions to the one-dimensional nonlinear Schroedinger equation under box or periodic boundary conditions are presented in analytic form for the case of attractive nonlinearity. A companion paper has treated the repulsive…
We extend to a specific class of systems of nonlinear Schr\"odinger equations (NLS) the theory of asymptotic stability of ground states already proved for the scalar NLS. Here the key point is the choice of an adequate system of modulation…
We study positive bound states for the semiclassical stationary nonlinear Schr\"odinger equation. We are especially interested in solutions which concentrate on a lower dimensional sphere. We adopt a purely variational approach which allows…
We study the existence and stability of localized states in the two-dimensional (2D) nonlinear Schrodinger (NLS)/Gross-Pitaevskii equation with a symmetric four-well potential. Using a fourmode approximation, we are able to trace the…
Competing nonlinearities, such as the cubic (Kerr) and quintic nonlinear terms whose strengths are of opposite signs (the coefficients in front of the nonlinearities), exist in various physical media (in particular, in optical and…
We derive several kinetic equations to model the large scale, low Fresnel number behavior of the nonlinear Schrodinger (NLS) equation with a rapidly fluctuating random potential. There are three types of kinetic equations the longitudinal,…
We obtain classification, solvability and nonexistence theorems for positive stationary states of reaction-diffusion and Schr\"odinger systems involving a balance between repulsive and attractive terms. This class of systems contains PDE…
The generalized (1+1)-D non-linear Schrodinger (NLS) theory with particular integrable boundary conditions is considered. More precisely, two distinct types of boundary conditions, known as soliton preserving (SP) and soliton non-preserving…
In this paper, we study the non-homogeneous nonlinear Schr\"{o}dinger system $$\left\{ \begin{array}{ll} -\triangle u_j+V_j(x) u_j=g_j(x,u_1,\cdots,u_m)+h_j(x),& x\in \Omega,\\ \\ u_j:=u_j(x)=0,& x\in \partial\Omega,\\ \\ j=1,2,\cdots,m,…
We reveal the universal effect of gauge fields on the existence, evolution, and stability of solitons in the spinor multidimensional nonlinear Schr\"{o}dinger equation. Focusing on the two-dimensional case, we show that when gauge field can…
All stationary solutions to the one-dimensional nonlinear Schroedinger equation under box and periodic boundary conditions are presented in analytic form. We consider the case of repulsive nonlinearity; in a companion paper we treat the…
We examine conditions for finite-time collapse of the solutions of the higher-order nonlinear Schr\"odinger (NLS) equation incorporating third-order dispersion, self-steepening, linear and nonlinear gain and loss, and Raman scattering; this…