2014/12/06 by Marco Bertola, Bertola, Marco, Pietro Giavedoni +1
Computer Science · Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Dynamics and Pattern Formation #Nonlinear Photonic Systems #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.1412.2273
openalex publication_date 2014/12/06 · openalex created_date 2022/08/29 · openalex updated_date 2026/07/28
Two-phase solutions of focusing NLS equation are classically constructed out\nof an appropriate Riemann surface of genus two, and expressed in terms of the\ncorresponding theta-function. We show here that in a certain limiting regime\nsuch solutions reduce to some elementary ones called "Solitons on unstable\ncondensate". This degeneration turns out to be conveniently studied by means of\nbasic tools from the theory of Riemann-Hilbert problems. In particular no\nacquaintance with Riemann surfaces and theta-function is required for such\nanalysis.\n