scholarly journals Internal control for a non-local Schrödinger equation involving the fractional Laplace operator

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Umberto Biccari
Keyword(s):  
Schrödinger Equation ◽  
Laplace Operator ◽  
Internal Control ◽  
Schrodinger Equation ◽  
Non Local ◽  
Fractional Laplace Operator

Solitary waves of the non-local Schrödinger equation with arbitrary refractive index

Optik ◽  
2021 ◽  
Vol 231 ◽  
pp. 166443
Author(s):  
Nikolay A. Kudryashov
Keyword(s):  
Refractive Index ◽  
Schrödinger Equation ◽  
Solitary Waves ◽  
Schrodinger Equation ◽  
Non Local

scholarly journals Rational solutions of the defocusing non-local nonlinear Schrödinger equation: asymptotic analysis and soliton interactions

2021 ◽  
Vol 477 (2254) ◽  
Author(s):  
Tao Xu ◽  
Lingling Li ◽  
Min Li ◽  
Chunxia Li ◽  
Xuefeng Zhang
Keyword(s):  
Schrödinger Equation ◽  
Asymptotic Analysis ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Algebraic Curves ◽  
Nonlinear Schrodinger Equation ◽  
Rational Solutions ◽  
Soliton Interactions ◽  
Nonlinear Schrödinger ◽  
Non Local

In this paper, we obtain the N th-order rational solutions for the defocusing non-local nonlinear Schrödinger equation by the Darboux transformation and some limit technique. Then, via an improved asymptotic analysis method relying on the balance between different algebraic terms, we derive the explicit expressions of all asymptotic solitons of the rational solutions with the order 1 ≤ N ≤ 4 . It turns out that the asymptotic solitons are localized in the straight lines or algebraic curves, and the exact solutions approach the curved asymptotic solitons with a slower rate than the straight ones. Moreover, we find that all the rational solutions exhibit just five different types of soliton interactions, and the interacting solitons are divided into two halves with each having the same amplitudes. Particularly for the curved asymptotic solitons, there may exist a slight difference for their velocities between at t and − t with certain parametric conditions. In addition, we reveal that the soliton interactions in the rational solutions with N ≥ 2 are stronger than those in the exponential and exponential-and-rational solutions.

scholarly journals Existence and multiplicity of solutions for a non-linear Schrödinger equation with non-local regional diffusion

2017 ◽  
Vol 58 (11) ◽  
pp. 111507 ◽  
Author(s):  
Claudianor O. Alves ◽  
César E. Torres Ledesma
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Multiplicity Of Solutions ◽  
Existence And Multiplicity ◽  
Non Linear ◽  
Non Local

scholarly journals CONTROL AND STABILIZATION OF THE NONLINEAR SCHRÖDINGER EQUATION ON RECTANGLES

2010 ◽  
Vol 20 (12) ◽  
pp. 2293-2347 ◽  
Author(s):  
LIONEL ROSIER ◽  
BING-YU ZHANG
Keyword(s):  
Schrödinger Equation ◽  
Boundary Conditions ◽  
Control Region ◽  
Internal Control ◽  
Schrodinger Equation ◽  
Exact Controllability ◽  
Neumann Boundary ◽  
Local Controllability ◽  
Boundary Controls ◽  
Semilinear Schrödinger Equation

This paper studies the local exact controllability and the local stabilization of the semilinear Schrödinger equation posed on a product of n intervals (n ≥ 1). Both internal and boundary controls are considered, and the results are given with periodic (resp. Dirichlet or Neumann) boundary conditions. In the case of internal control, we obtain local controllability results which are sharp as far as the localization of the control region and the smoothness of the state space are concerned. It is also proved that for the linear Schrödinger equation with Dirichlet control, the exact controllability holds in H-1(Ω) whenever the control region contains a neighborhood of a vertex.

scholarly journals Internal control of the Schrödinger equation

2014 ◽  
Vol 4 (2) ◽  
pp. 161-186 ◽  
Author(s):  
Camille Laurent ◽  
Keyword(s):  
Schrödinger Equation ◽  
Internal Control ◽  
Schrodinger Equation

Coherent quantum hollow beam creation in a plasma wakefield accelerator

2013 ◽  
Vol 79 (4) ◽  
pp. 397-403 ◽  
Author(s):  
D. JOVANOVIĆ ◽  
R. FEDELE ◽  
F. TANJIA ◽  
S. DE NICOLA ◽  
M. BELIĆ
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Mean Field ◽  
Magnetoactive Plasma ◽  
Particle Beam ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Coupled Equations ◽  
Non Local ◽  
Plasma Wakefield

AbstractA theoretical investigation of the propagation of a relativistic electron (or positron) particle beam in an overdense magnetoactive plasma is carried out within a fluid plasma model, taking into account the individual quantum properties of beam particles. It is demonstrated that the collective character of the particle beam manifests mostly through the self-consistent macroscopic plasma wakefield created by the charge and the current densities of the beam. The transverse dynamics of the beam–plasma system is governed by the Schrödinger equation for a single-particle wavefunction derived under the Hartree mean field approximation, coupled with a Poisson-like equation for the wake potential. These two coupled equations are subsequently reduced to a nonlinear, non-local Schrödinger equation and solved in a strongly non-local regime. An approximate Glauber solution is found analytically in the form of a Hermite–Gauss ring soliton. Such non-stationary (‘breathing’ and ‘wiggling’) coherent structure may be parametrically unstable and the corresponding growth rates are estimated analytically.

scholarly journals Weakly non-local fluid mechanics: the Schrödinger equation

2005 ◽  
Vol 462 (2066) ◽  
pp. 541-557 ◽  
Author(s):  
Peter Ván ◽  
Tamás Fülöp
Keyword(s):  
Fluid Dynamics ◽  
Schrödinger Equation ◽  
Fluid Mechanics ◽  
Schrodinger Equation ◽  
Second Law Of Thermodynamics ◽  
Second Law ◽  
Local Extension ◽  
Specific Entropy ◽  
Pressure Term ◽  
Non Local

A weakly non-local extension of ideal fluid dynamics is derived from the Second Law of thermodynamics. It is proved that in the reversible limit, the additional pressure term can be derived from a potential. The requirement of the additivity of the specific entropy function determines the quantum potential uniquely. The relation to other known derivations of the Schrödinger equation (stochastic, Fisher information, exact uncertainty) is clarified.

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