Spectrally accurate space-time solution of Manakov systems
arXiv:1910.06040 · doi:10.1016/j.cam.2020.112918
Abstract
In this paper, we study the numerical solution of Manakov systems by using a spectrally accurate Fourier decomposition in space, coupled with a spectrally accurate time integration. This latter relies on the use of spectral Hamiltonian boundary Value Methods. The used approach allows to conserve all the physical invariants of the systems. Some numerical tests are reported.
arXiv comment29 pages (typo in equation (20) fixed)
References in corpus (19)
- Dark solitons in atomic Bose-Einstein condensates: from theory to experiments
- Optical solitons in graded-index multimode fiber
- Nonlinear Propagation in Multimode and Multicore Fibers: Generalization of the Manakov Equations
- Hamiltonian Boundary Value Methods (Energy Conserving Discrete Line Integral Methods)
- Soliton trapping in multimode fibers with random mode coupling
- A unifying framework for the derivation and analysis of effective classes of one-step methods for ODEs
- A note on the efficient implementation of Hamiltonian BVMs
- Energy conservation issues in the numerical solution of the semilinear wave equation
- Analisys of Hamiltonian Boundary Value Methods (HBVMs): a class of energy-preserving Runge-Kutta methods for the numerical solution of polynomial Hamiltonian systems
- Spectrally accurate space-time solution of Hamiltonian PDEs
- Efficient implementation of Gauss collocation and Hamiltonian Boundary Value Methods
- On the effectiveness of spectral methods for the numerical solution of multi-frequency highly-oscillatory Hamiltonian problems
- Multiple invariants conserving Runge-Kutta type methods for Hamiltonian problems
- High-order energy-conserving Line Integral Methods for charged particle dynamics
- Energy-conserving methods for Hamiltonian Boundary Value Problems and applications in astrodynamics
- Vector Nonlinear Schrödinger Equation on the half-line
- Line Integral solution of Hamiltonian PDEs
- A note on the continuous-stage Runge-Kutta-(Nyström) formulation of Hamiltonian Boundary Value Methods (HBVMs)
- Line Integral Solution of Hamiltonian Systems with Holonomic Constraints