For the generalized statistical mechanics based on the Tsallis entropy, a variational perturbation approximation method with the principle of minimal sensitivity is developed by calculating the generalized free energy up to the third order in variational perturbation expansion. The approximation...

We investigate the propagation of ultrashort solitons in fiber-optic systems in the presence of the soliton self-frequency shift effect. It is demonstrated that both the self-frequency shift and the background instability can be effectively controlled using spectral filters of moderate strength...

We solve analytically the Merton's problem of an investor with time additive power utility. For general state dynamics, we prove existence of two power series representations of the relevant optimal policies and value functions, which hold for all admissible risk aversion parameters. We...