2010/09/24 by Trevor Potter, Potter, Trevor
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Cold Atom Physics and Bose-Einstein Condensates #FOS: Mathematics #FOS: Physical sciences #Nonlinear Photonic Systems #Numerical Analysis (math.NA) #Pattern Formation and Solitons (nlin.PS)
paper · pdf · doi:10.48550/arxiv.1009.4910
openalex publication_date 2010/09/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
We consider several solitons moving in a slowly varying external field. We show that the effective dynamics obtained by restricting the full Hamiltonian to the finite dimensional manifold of N-solitons (constructed when no external field is present) provides a remarkably good approximation to the actual soliton dynamics. That is quantified as an error of size h2 where h is the parameter describing the slowly varying nature of the potential. This also indicates that previous mathematical results of Holmer-Zworski for one soliton are optimal. For potentials with unstable equilibria the Ehrenrest time, log(1/h)/h , appears to be the natural limiting time for these effective dynamics. We also show that the results of Holmer-Perelman-Zworski for two mKdV solitons apply numerically to a larger number of interacting solitons. We illustrate the results by applying the method with the external potentials used in Bose-Einstein soliton train experiments of Strecker et. al.