Results 11 to 20 of about 167 (129)
Semidiscrete Vortex Solitons [PDF]
Advanced Photonics Research, 2021 A possibility of creation of stable optical solitons combining one continuous and one discrete coordinates, with embedded vorticity, in an array of planar waveguides with intrinsic cubic–quintic (CQ) nonlinearity is demonstrated. The same system may be realized in terms of the spatiotemporal light propagation in an array of tunnel‐coupled optical ...
Xiaoxi Xu +6 more
openaire +3 more sources
A New Technique for Preserving Conservation Laws [PDF]
, 2021 This paper introduces a new symbolic-numeric strategy for finding semidiscretizations of a given PDE that preserve multiple local conservation laws. We prove that for one spatial dimension, various one-step time integrators from the literature preserve ...
Frasca-Caccia, Gianluca +5 more
core +2 more sources
Semidiscrete Quantum Droplets and Vortices [PDF]
Physical Review Letters, 2019 We consider a binary bosonic condensate with weak mean-field (MF) residual repulsion, loaded in an array of nearly one-dimensional traps coupled by transverse hopping. With the MF force balanced by the effectively one-dimensional attraction, induced in each trap by the Lee-Hung-Yang correction (produced by quantum fluctuations around the MF state ...
Xiliang Zhang +7 more
openaire +3 more sources
Variational Laplacians for semidiscrete surfaces [PDF]
Advances in Computational Mathematics, 2016 The authors propose a variational definition of the Laplacian on semidiscrete surfaces. Recall that the classical Laplace-Beltrami operator on Riemannian manifolds can be defined via the Dirichlet energy functional with an obvious connection to the mean curvature normal vector.
Carl, Wolfgang, Wallner, Johannes
openaire +4 more sources
Exponentially accurate Hamiltonian embeddings of symplectic A-stable Runge--Kutta methods for Hamiltonian semilinear evolution equations [PDF]
, 2016 We prove that a class of A-stable symplectic Runge--Kutta time semidiscretizations (including the Gauss--Legendre methods) applied to a class of semilinear Hamiltonian PDEs which are well-posed on spaces of analytic functions with analytic initial data ...
Wulff, Claudia, Oliver, M
core +2 more sources
On the numerical approximation of Boussinesq/Boussinesq systems for internal waves [PDF]
, 2023 Producción CientíficaThe present paper is concerned with the numerical approximation of a three-parameter family of Boussinesq systems. The systems have been proposed as models of the propagation of long internal waves along the interface of a two-layer ...
Dougalis, Vassilios A. +2 more
core +2 more sources
Semidiscretization for a nonlocal parabolic problem [PDF]
International Journal of Mathematics and Mathematical Sciences, 2005 A time discretization technique by Euler forward scheme is proposed to deal with a nonlocal parabolic problem. Existence and uniqueness of the approximate solution are proved.
Abderrahmane El Hachimi +1 more
openaire +3 more sources
Error estimates for finite element approximations of elliptic control problems [PDF]
, 2007 We investigate finite element approximations of one-dimensional elliptic control problems. For semidiscretizations and full discretizations with piecewise constant controls we derive error estimates in the maximum ...
Bräutigam, Nils +2 more
core +1 more source
, 2022 For the general class of residual distribution (RD) schemes, including many finite element (such as continuous/discontinuous Galerkin) and flux reconstruction methods, an approach to construct entropy conservative/ dissipative semidiscretizations by ...
Ranocha, Hendrik; https://orcid.org/ +2 more
core +2 more sources
Semidiscretization in time for parabolic problems [PDF]
Mathematics of Computation, 1979 We study the error to the discretization in time of a parabolic evolution equation by a single-step method or by a multistep method when the initial condition is not regular.
openaire +1 more source