相关论文: Control results for a model of resonant interactio…
In this work we study the initial boundary value problem associated with the coupled Schr\"odinger equations {with quadratic nonlinearities, that appears in nonlinear optics}, on the half-line. We obtain local well-posedness for data {in…
An existence result is proved for a nonlinear diffusion problem of phase-field type, consisting of a parabolic system of two partial differential equations, complemented by Neumann homogeneous boundary conditions and initial conditions.…
This study deals with the analysis of the Cauchy problem of a general class of nonlocal nonlinear equations modeling the bi-directional propagation of dispersive waves in various contexts. The nonlocal nature of the problem is reflected by…
Striped Turing patterns and solitary band and disk structures are constructed using a three-variable multiscale model with cubic nonlinearity and global control. The existence and stability conditions of regular structures are analysed…
Van der Waals interactions are ubiquitous and they play an important role for the stability of materials. Current understanding of this type of coupling is based on linear response theory, while optical nonlinearities are rarely considered…
In this paper, we study a coupled nonlinear Schr\"odinger system with small initial data in a product space. We establish a modified scattering of the solutions of this system and we construct a modified wave operator. The study of the…
In this work, we found a non trivial topology to achieve the controllability for linear and nonlinear system in finite or infinite time horizon. We give several examples illustrating this topologizing method for the controllability results.…
We study the effects of the generic weak nonlinear loss on fast two-pulse interactions in linear waveguides. The colliding pulses are described by a system of coupled Schr\"odinger equations with a purely nonlinear coupling in the presence…
For nonlinear dispersive systems, the nonlinear Schr\"odinger (NLS) equation can usually be derived as a formal approximation equation describing slow spatial and temporal modulations of the envelope of a spatially and temporally…
We investigate a new class of nonlinear control systems of O.D.E., which are not feedback linearizable in general. Our class is a generalization of the well-known feedback linearizable systems, and moreover it is a generalization of the…
An analysis of discrete systems is important for understanding of various physical processes, such as excitations in crystal lattices and molecular chains, the light propagation in waveguide arrays, and the dynamics of Bose-condensate…
We prove global internal controllability in large time for the nonlinear Schr\"odinger equation on some compact manifolds of dimension 3. The result is proved under some geometrical assumptions : geometric control and unique continuation.…
We develop modulation theory for undular bores (dispersive shock waves) in the framework of the Gardner, or extended Korteweg--de Vries, equation, which is a generic mathematical model for weakly nonlinear and weakly dispersive wave…
We consider the defocusing nonlinear Schr{\"o}dinger equation with a gauge invariant power-like nonlinearity. We prove global dispersive estimates in a semi-classical scaling, after rescaling the solution thanks to a suitable distorsion of…
For the first time, a nonlinear Schr\"odinger equation of the general form is considered, depending on time and two spatial variables, the potential and dispersion of which are specified by two arbitrary functions. This equation naturally…
We present trapped solitary wave solutions of a coupled nonlinear Schr\"odinger system in $1$+$1$ dimensions in the presence of an external, supersymmetric and complex $\mathcal{PT}$-symmetric potential. The Schr\"odinger system this work…
In this paper we introduce a system coupling a nonlinear Schr\"odinger equation with a system of viscoelasticity, modeling the interaction between short and long waves, acting for instance on media like plasmas or polymers. We prove the…
In this paper we study the Cauchy problem associated to the Maxwell-Schr\"odinger system with a defocusing pure-power non-linearity. This system has many applications in physics, for instance in the description of a charged non-relativistic…
Waveguides subject to spatiotemporal modulations are known to exhibit nonreciprocal vibration transmission, whereby interchanging the locations of the source and receiver change the end-to-end transmission characteristics. The scenario of…
Various controllability conditions have been obtained by researchers for heterogeneous networked systems with linear dynamics. However, the literature for nonlinear, heterogeneous networked systems is comparatively less. In this paper we…