  The goal of this work is to determine classes of traveling solitary wave
solutions for Lattice Boltzmann schemes by means of an hyperbolic ansatz. It is
shown that spurious solitary waves can occur in finite-difference solutions of
nonlinear wave equation. The occurence 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 have 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 solutions of the original continuous
equations. This paper extends our previous work about classical schemes to
Lattice Boltzmann schemes.
