The consistence between the stokes wave theory and general wave theory

The consistence between the Stokes wave theory and general wave theory is examined in this study. As well known, the nonlinear terms of Stokes wave are generated by the self-interaction of first-order wave. On the other side, using the general wave theory one can also obtain the nonlinear solutions according to the interaction of n waves with the same amplitude, frequency and phase. It is found that the inconsistence between these two wave trains arises due to the subharmonic effects included in general wave theory but not considered in the Stokes theory. In conclusion, these two theories are substantially different unless the Bernoulli constants are properly chosen for mathematical equivalence.