Invariants and numerical methods for ODEs
Proceedings of the eleventh annual international conference of the Center for Nonlinear Studies on Experimental mathematics : computational issues in nonlinear science: computational issues in nonlinear science
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Dissipation in Hamiltonian systems: decaying cnoidal waves
SIAM Journal on Mathematical Analysis
SIAM Journal on Numerical Analysis
Inversion of the linearized Korteweg-de Vries equation at the multi-soliton solutions
Zeitschrift für Angewandte Mathematik und Physik (ZAMP)
Backward Error Analysis for Numerical Integrators
SIAM Journal on Numerical Analysis
Geometric integrators for the nonlinear Schrödinger equation
Journal of Computational Physics
On Symplectic and Multisymplectic Schemes for the KdV Equation
Journal of Scientific Computing
Simulation of coherent structures in nonlinear Schrödinger-type equations
Journal of Computational Physics
A numerical scheme for periodic travelling-wave simulations in some nonlinear dispersive wave models
Journal of Computational and Applied Mathematics
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This paper is devoted to study the error growth of numerical time integrators for N-phase or N-band quasi-periodic (in time) solutions of the periodic Korteweg-de Vries equation. It is shown that the preservation, through numerical time integration, of conserved quantities of the periodic problem of the equation, may be an element to take into account in the selection of the numerical method. We explain why the inclusion of these properties of conservation provides a better error propagation. In particular, we emphasize how the preservation of invariants makes influence in the simulation of some physical parameters of the waves.