  The goal of this work is to determine classes of travelling solitary wave
solutions for a differential approximation of a finite difference scheme by
means of a hyperbolic ansatz. It is shown that spurious solitary waves can
occur in finite-difference solutions of nonlinear wave equation. The occurance
of such a spurious solitary wave, 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 (solitary waves in the present case) that are
not solution of the original continuous equations. This paper extends our
previous work about classical schemes to dispersion-relation preserving
schemes.
