Stability analysis for solitons in planar waveguides, fibres and couplers using Hamiltonian concepts

The use of Hamiltonian-versus-energy (HVE) curves for localised optical soliton solutions is a powerful method for studying systems with an infinite number of degrees of freedom. These curves are useful for analysing the range of existence and stability of solitons. Detailed analysis of HVE curves and their special points are given. The authors illustrate their conclusions with several new examples which show the usefulness of the concept. The main example is related to non-Kerr-type solitons in planar waveguides, although examples of solitons in fibres and couplers are also provided. Specifically it is shown that, in the special case of a two-dimensional beam in a Kerr medium, the curve contracts to a point. It is also demonstrated that. in some cases, it is possible to find the Hamiltonian and energy without knowledge of the functional form of the soliton itself. The authors explain how this can be used in various aspects of soliton theory.