Optimization strategy to find shapes of soliton molecules

Frequently, a certain solution of a nonlinear wave equation is of interest, but no analytic form is known, and one must work with approximations. We introduce a search strategy to find solutions of the propagation of soliton molecules in a dispersion-managed optical fiber and to determine their shape with some precision. The strategy compares shapes before and after propagation and invokes an optimization routine to minimize the difference. The scheme is designed to be implemented in an experiment so that all fiber parameters are taken into account. Here, we present a full numerical study and a verification of convergence; we validate the method with cases of known solutions. We also compare the performance of two optimization procedures, the Nelder–Mead simplex method and a genetic algorithm.