Families of travelling wave solutions have been studied in a one-dimen
sional kink-bearing model with a nonlinear intersite coupling. The val
ue of the soliton velocity depends on the parameters of the system suc
h as an anharmonicity parameter and the barrier height of the on-site
potential, to which the chain is subjected. These dependencies have be
en studied numerically using a pseudo-spectral method. The solution sp
ace of the bound state lattice solitons has an interesting bifurcation
structure.