Model for relating coupled power equations to coupled amplitude equations

Following a suggestion of H. E. Rowe, the first-order system of coupled differential equations with the independent variables representing amplitudes of coupled modes (the so-called coupled mode equations) has been rigorously transformed into similar equations with the independent variables representing the power in the coupled modes for the case where the amplitude coupling coefficient is a Gaussian random process with a white noise spectrum and zero mean value. Coupled mode equations in power have proven useful, and this work provides formal justification and identification of the variables and parameters The equations may allow one to approach coupled-mode problems directly for statistical results