Spurious lattice solitons for linear finite difference schemes
Résumé
The goal of this work is to show that lattice traveling solitary wave are solution of the general linear finite-differenced version of the linear advection equation. The occurance of such a spurious solitary waves, 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 has a structural instability of the scheme, since the space of solutions spanned by the numerical scheme encompasses types of solutions (lattice solitary waves in the present case) that are not solution of the original continuous equations.
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