Soliton Lattice and Single Soliton Solutions of the Associated Lamé and Lamé Potentials

Details Soliton Lattice and Single Soliton Solutions of the Associated Lamé and Lamé Potentials Soliton Lattice and Single Soliton Solutions of the Associated Lamé and Lamé Potentials

2004-01-22

arxiv.org/abs/nlin/0401032v1

J.Math.Phys. 45 (2004) 2323-2337

Nonlinear Sciences

Pattern Formation and Solitons

23 pages, 5 figures. Submitted to J. Math. Phys

Scientific paper

We obtain the exact nontopological soliton lattice solutions of the Associated Lam\'e 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 Lam\'e 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 Lam\'e equation, and also the sine-Gordon soliton solution.

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