Soliton lattice and single soliton solutions of the associated Lamé and Lamé potentials

Abstract

We obtain the exact nontopological soliton lattice solutions of the associated Lamé equation in different parameter regimes and compute the corresponding energy for each of these solutions. We show that in specific limits these solutions give rise to nontopological (pulse-like) single solitons, as well as to different types of topological (kink-like) single soliton solutions of the associated Lamé equation. Following Manton, we also compute, as an illustration, the asymptotic interaction energy between these soliton solutions in one particular case. Finally, in specific limits, we deduce the soliton lattices, as well as the topological single soliton solutions of the Lamé equation, and also the sine-Gordon soliton solution.