  Parametric simultaneous solitary wave (simulton) excitations are shown
possible in nonlinear lattices. Taking a one-dimensional diatomic lattice with
a cubic potential as an example we consider the nonlinear coupling between the
upper cutoff mode of acoustic branch (as a fundamental wave) and the upper
cutoff mode of optical branch (as a second harmonic wave). Based on a
quasi-discreteness approach the Karamzin-Sukhorukov equations for two slowly
varying amplitudes of the fundamental and the second harmonic waves in the
lattice are derived when the condition of second harmonic generation is
satisfied. The lattice simulton solutions are explicitly given and the results
show that these lattice simultons can be nonpropagating when the wave vectors
of the fundamental wave and the second harmonic waves are exactly at $\pi/a$
(where $a$ is the lattice constant) and zero, respectively.
