English

Soliton Lattice and Single Soliton Solutions of the Associated Lam\'e and Lam\'e Potentials

Pattern Formation and Solitons 2015-06-26 v1 Other Condensed Matter Mathematical Physics math.MP

Abstract

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.

Keywords

Cite

@article{arxiv.nlin/0401032,
  title  = {Soliton Lattice and Single Soliton Solutions of the Associated Lam\'e and Lam\'e Potentials},
  author = {Ioana Bena and Avinash Khare and Avadh Saxena},
  journal= {arXiv preprint arXiv:nlin/0401032},
  year   = {2015}
}

Comments

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