A nonlinear transmission system for the laser pulse amplifier is discussed. Using the generalized functional-variational iteration theory and method, the corresponding approximate solution of the system is obtained, which facilitates the design of laser pulse amplifiers.

A class of nonlinear generalized Duffing equation for disturbed oscillator is considered. Firstly, the typical Duffing equation is solved. Then approximate solutions to the nonlinear Duffing equation for disturbed oscillators in stochastic resonance is obtained using the generalized functional variation principle, and the uniform validity is proved.

For an inhomogeneous quantum magnetoplasma system in the atmospheric environment with density and temperature gradient, a two-dimensional nonlinear fluid dynamic perturbation equation is studied in the case where the collision frequency between ions and neutrals is small. The approximate solution of the potential in the dense astrophysical environment is obtained.

Using Mawhin's continuation theorem, we discussed the existence of periodic solution for a class of nonlinear problem, and then investigated the problem of periodic solution of sport model of plasmas particle in the process of magnetosphere-ionosphere coupling. A result on the existence of periodic solution to the model is obtained.

A class of transfer models for femtosecond pulse laser on nano metal film has been investigated. First, we solve the reduced solution. And then, the arbitrary order asymptotic solution of corresponding model is obtained by using the perturbation theory and method. Finally, the behavior of the solution is discussed.