Related papers: Nonlinearity Management in Higher Dimensions
We consider time-dependent Schroedinger equations in one dimension with double well potential and an external nonlinear perturbation. If the initial state belongs to the eigenspace spanned by the eigenvectors associated to the two lowest…
Fractional nonlinear differential equations present an interplay between two common and important effective descriptions used to simplify high dimensional or more complicated theories: nonlinearity and fractional derivatives. These…
In this note, we generalize the nonlinearity-recovery result in [7] for classical cubic nonlinear Schr\"odinger equations to higher-order Schr\"odinger equations with a more general nonlinearity. More precisely, we consider a…
We consider the mass-critical focusing nonlinear Schrodinger equation in the presence of an external potential, when the nonlinearity is inhomogeneous. We show that if the inhomogeneous factor in front of the nonlinearity is sufficiently…
This paper addresses the problem of averaged controllability for the time-fractional Schrodinger equation, where the quantum diffusivity parameter is a random variable with a general probability distribution. First, by exploiting the…
In this paper we concentrate on the analysis of the critical mass blowing-up solutions for the cubic focusing Schr\"odinger equation with Dirichlet boundary conditions, posed on a plane domain. We bound the blow-up rate from below, for…
In this paper, we study the focusing nonlinear Schr\"odinger equation with exponential nonlinearities \[ i \partial_t u + \Delta u = - \left(e^{4\pi |u|^2} - 1 - 4\pi \mu |u|^2 \right) u, \quad u(0) = u_0 \in H^1, \quad (t,x) \in \mathbb{R}…
We study the influence of a multiplicative Gaussian noise, white in time and correlated in space, on the blow-up phenomenon in the supercritical nonlinear Schrodinger equation. We prove that any sufficiently regular and localized…
We investigate the long time dynamics of the nonlinear Schr\"odinger equation (NLS) with combined powers on the waveguide manifold $\mathbb{R}^d\times\mathbb{T}$. Different from the previously studied NLS-models with single power on the…
Assessment of the degree of boundedness/stability of multidimensional nonlinear systems with time-dependent and nonperiodic coefficients is an important problem in various applied areas which has no adequate resolution yet. Most of the…
We consider a two-component system of cubic nonlinear Schr\"odinger equations in one space dimension. We show that each component of the solutions to this system behaves like a free solution in the large time, but there is a strong…
A control problem with terminal overdetermination is considered for the higher order nonlinear Schr\"odinger equation on a bounded interval. The boundary condition on the space derivative is chosen as the control. Results on global…
The initial value problem is considered for a higher order nonlinear Schr\"odinger equation with quadratic nonlinearity. Results on existence and uniqueness of weak solutions are obtained. In the case of an effective at infinity additional…
Consider the initial value problem for cubic derivative nonlinear Schr\"odinger equations in one space dimension. We provide a detailed lower bound estimate for the lifespan of the solution, which can be computed explicitly from the initial…
We conduct an experimental investigation of nonlinearity management in optics using femtosecond pulses and layered Kerr media consisting of glass and air. By examining the propagation properties over several diffraction lengths, we show…
We consider semidiscrete finite differences schemes for the periodic Scr\"odinger equation in dimension one. We analyze whether the space-time integrability properties observed by Bourgain in the continuous case are satisfied at the…
We consider nonlinear Schrodinger equations with either local or nonlocal nonlinearities. In addition, we include periodic potentials as used, for example, in matter wave experiments in optical lattices. By considering the corresponding…
We consider the nonlinear Schr\"odinger equation on a unit ball in one and two dimensions with Dirichlet boundary conditions, which have stabilizing effect on solutions behavior. In particular, we confirm that the ground state solutions are…
We consider the nonlinear Schr\"odinger equation \[ u_t = i \Delta u + | u |^\alpha u \quad \mbox{on ${\mathbb R}^N $, $\alpha>0$,} \] for $H^1$-subcritical or critical nonlinearities: $(N-2) \alpha \le 4$. Under the additional technical…
We consider a nonlinear Schr\"odinger equation with double power nonlinearity, where one power is focusing and mass critical and the other mass sub-critical. Classical variational arguments ensure that initial data with mass less than the…