Spurious lattice solitons for linear finite difference schemes

Claire David (1)

1 LJLL - Laboratoire Jacques-Louis Lions

The goal of this work is to show that lattice solitons are solution of the general linear finite-differenced version of the linear advection equation. The occurance of such a spurious solitons, which exhibits a very long life time, results in a non-vanishing numerical error for arbitrary time in unbounded numerical domain. Such a behavior is referred here to have a structural instability of the scheme, since the space of solutions spanned by the numerical scheme encompasses types of solutions that are not solutions of the original continuous equations. What can be of noticeable interest is the link established between linear finite difference schemes and the DST equation (Discrete Self Trapping Equation).

Mots clés: spurious lattice solitary waves; Numerical schemes; spurious lattice solitary waves.

Domaines: Equations aux dérivées partielles [math.AP]

Claire David. Spurious lattice solitons for linear finite difference schemes. 2013. ⟨hal-00770992⟩