2021/05/10 by Charles W. Robson, Robson, Charles W., Fabio Biancalana +1
Mathematics · Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Photonic Systems #Pattern Formation and Solitons (nlin.PS) #Strong Light-Matter Interactions #math-ph #math.MP #nlin.PS
paper · pdf · doi:10.48550/arxiv.2105.04498
arxiv created 2021/05/10 · openalex publication_date 2021/05/10 · arxiv updated 2021/05/11 · openalex created_date 2021/05/24 · openalex updated_date 2026/07/28
We investigate a novel mapping between solutions to several members of the Klein-Gordon family of equations and solutions to equations describing their reductions via the slowly varying envelope approximation. This mapping creates a link between the study of interacting relativistic fields and that of systems more amenable to laboratory-based analogue research, the latter described by nonlinear Schrödinger equations. A new evolution equation is also derived, emerging naturally from the sine-Gordon formula, possessing a Bessel-function nonlinearity; numerical investigations show that solutions to this novel equation include quasi-solitary waves, breather solutions, along with pulse splittings and recombinations.