2004/01/22 by Ioana Bena, Avinash Khare, Avadh Saxena · 3 citations
Mathematics · Physics and Astronomy · #Dissipative soliton #Exact solutions in general relativity #Lattice (music) #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics #Soliton #Topological defect #cond-mat.other #math-ph #math.MP #nlin.PS #sine-Gordon equation
paper · pdf · doi:10.1063/1.1738952
published in Journal of Mathematical Physics 45(6), 2323-2337 (American Institute of Physics) · 23 pages, 5 figures. Submitted to J. Math. Phys
arxiv created 2004/01/22 · openalex publication_date 2004/05/14 · arxiv updated 2015/06/26 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.