Variational analysis of solitary waves in a homogeneous cubic-quintic nonlinear medium

Fundamental solitary waves in a cubic-quintic nonlinear medium are investigated both numerically and variationally. An equivalent particle model is used to understand the behaviour of the numerical solutions, and while a super-Gaussian trial function is found to have only a limited range of applicability in the variational analysis, a super-sech trial function is found to match the numerical solutions well for all input powers. Various limits are also investigated.