Generalized variational approximations for the optical soliton

Considering a basic process of the soliton-effect pulse compression, we perform systematic comparison of analytical predictions based on the variational approximation (VA) versus direct simulations. We demonstrate that the traditional VA provides a good accuracy in predicting the optimum compression length only for rather small compression degrees. We put forward modifications of VA based on two new ansätze, which differ from the traditional one by an assumed phase pattern. One modification yields only a slight improvement in the accuracy, but the other one, being suggested by numerical findings, and being as analytically tractable as the traditional approximation, drastically improves the accuracy just for large compression degrees, although being essentially worse for weak compression.