Practical application of the adiabatic approximation and its simplified version for solving a nonintegrable system of nonlinear Schrödinger equations

Using the example of the interaction of two cnoidal waves with essentially different periods, we compare the results of the application of the adiabatic approximation and its simplified version in the process of solving a nonintegrable system of nonlinear Schrödinger equations. The time boundary of the region of applicability of the simplified adiabatic-approximation version is estimated.