This short paper deals with coupled nonlinear wave equations, involving two dependent variables u(x,t) and v(x,t), originally proposed by M. Ito
[Phys. Lett. A 91, 335-338 (1982)] and later generalized by S. Kawamoto
[J. Phys. Soc. Jen. 53, 1203-1205 (1984)]. The authors study their traveling-wave solutions by introducing a stream function
. It was shown that if one of the solutions is a function of (x-ct), the other must exhibit the same dependence of variables. Furthermore, inclusion of cubic nonlinear terms was considered, and corresponding solutions of the traveling-wave type have also been obtained.