title: Comparison of Lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems.
abstract: For equations that cannot be solved exactly, the trial function approach to modelling soliton solutions represents a useful approximate technique. It has to be supplemented with the Lagrangian technique or the method of moments to obtain a finite dimensional dynamical system which can be analyzed more easily than the original partial differential equation. We compare these two approaches. Using the cubic-quintic complex Ginzburg-Landau equation as an example, we show that, for a wide class of plausible trial functions, the same system of equations will be obtained. We also explain where the two methods differ.
authors.affiliation: Optical Sciences Group, Research School of Physical Sciences and Engineering, The Australian National University, Canberra, Australian Capital Territory 0200, Australia.
authors.forename: Adrian
authors.initials: A
authors.lastname: Ankiewicz
authors.forename: Nail
authors.initials: N
authors.lastname: Akhmediev
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D008962:Models, Theoretical; D017711:Nonlinear Dynamics; D009991:Oscillometry / Q000379:methods*