Formula_7284

\[\left.\begin{array}{rl}K_{1}\left(F_{1}\right) & =\frac{\gamma_{1}}{2 \pi} \frac{\partial}{\partial \tau} \int_{0}^{2 \pi} F_{2}(\eta, x, t) F_{3}(\tau+\eta, x, t) d \eta, \\K_{2}\left(F_{2}\right) & =\frac{\gamma_{2}}{2 \pi} \frac{\partial}{\partial \tau} \int_{0}^{2 \pi} F_{1}(\eta, x, t) F_{3}(\tau+\eta, x, t) d \eta, \\K_{3}\left(F_{3}\right) & =\frac{\gamma_{3}}{2 \pi} \frac{\partial}{\partial \tau} \int_{0}^{2 \pi} F_{1}(\eta, x, t) F_{2}(\tau-\eta, x, t) d \eta, \\K_{j}\left(F_{j}\right) & =\frac{d F_{j}}{d t_{j}}+\alpha_{j} F_{j} \frac{\partial F_{j}}{\partial \tau}+\beta_{j} \frac{\partial^{3} F_{j}}{\partial \tau^{3}}, \\\left.F_{m}\right|_{t=0} & =\varphi_{m}^{0}(x) \exp (i \tau)+\text { к.c., } \quad m=1,2,\left.\quad F_{3}\right|_{t=0}=0 .\end{array}\right\}\]