Numerical computation of soliton dynamics for NLS equations in a driving potential.
Numerical computation of solitons for optical systems
In this paper, we present numerical methods for the determination of solitons, that consist in spatially localized stationary states of nonlinear scalar equations or coupled systems arising in nonlinear optics. We first use the well-known shooting method in order to find excited states (characterized by the number of nodes) for the classical nonlinear Schrödinger equation. Asymptotics can then be derived in the limits of either large are large nonlinear exponents . In a second part, we compute...
Numerical computation of solitons for optical systems
In this paper, we present numerical methods for the determination of solitons, that consist in spatially localized stationary states of nonlinear scalar equations or coupled systems arising in nonlinear optics. We first use the well-known shooting method in order to find excited states (characterized by the number k of nodes) for the classical nonlinear Schrödinger equation. Asymptotics can then be derived in the limits of either large k are large nonlinear exponents σ. In a second part, we compute...
Numerical computation of the eigenvalues for the spheroidal wave equation with accurate error estimation by matrix method.
Numerical Computation of the Fourier Transform Using Laguerre Functions and the Fast Fourier Transform.
Numerical computations for solidification problems with change of volume
Numerical condition of polynomials in different forms.
Numerical conformal mappings of unbounded multiply-connected domains using the charge simulation method.
Numerical considerations of a hybrid proximal projection algorithm for solving variational inequalities
In this paper, some ideas for the numerical realization of the hybrid proximal projection algorithm from Solodov and Svaiter [22] are presented. An example is given which shows that this hybrid algorithm does not generate a Fejér-monotone sequence. Further, a strategy is suggested for the computation of inexact solutions of the auxiliary problems with a certain tolerance. For that purpose, ε-subdifferentials of the auxiliary functions and the bundle trust region method from Schramm and Zowe [20]...
Numerical controllability of the wave equation through primal methods and Carleman estimates
This paper deals with the numerical computation of boundary null controls for the 1D wave equation with a potential. The goal is to compute approximations of controls that drive the solution from a prescribed initial state to zero at a large enough controllability time. We do not apply in this work the usual duality arguments but explore instead a direct approach in the framework of global Carleman estimates. More precisely, we consider the control that minimizes over the class of admissible null...
Numerical determination of a canonical form of a symplectic matrix.
Numerical Differentation of Functions of Very Many Variables.
Numerical Differentiation Procedures for Non-Exact Data.
Numerical discrete algorithm for some nonlinear problems.
Numerical Error Bounds for Fourth Order Boundary Value Problems, Simultaneous Estimation of u(x) and u"(x).
Numerical Evaluation of Integrals of Periodic Functions with Cauchy and Poisson Type Kernels.
Numerical evidence for a conjecture in real algebraic geometry.
Numerical evidence of nonuniqueness in the evolution of vortex sheets
We consider a special configuration of vorticity that consists of a pair of externally tangent circular vortex sheets, each having a circularly symmetric core of bounded vorticity concentric to the sheet, and each core precisely balancing the vorticity mass of the sheet. This configuration is a stationary weak solution of the 2D incompressible Euler equations. We propose to perform numerical experiments to verify that certain approximations of this flow configuration converge to a non-stationary...
Numerical experiments in Fourier asymptotics of Cantor measures and wavelets.
Numerical experiments with algebraic multilevel preconditioners.