Large signals in nonlinear fiber optics (A01)

• Subject Area: Mathematics
• Term: since 2015
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 258734477

The propagation of signals in long glass fibre cables is effectively described by a one-dimensional cubic nonlinear Schrödinger equation. The aim of the project is to establish global wellposedness for large classes of non-decaying and non-periodic signals. We are particularly interested in initial data in modulation spaces and in initial data that are sums of a periodic and a local signal, focusing, in regularity as low as possible. Based on local results we need for global results in an essential way suitable new conserved, or nearly conserved, quantities. Moreover, we shall study the long-time behavior of such solutions.

• DFG Programme: Collaborative Research Centres
• Subproject of: SFB 1173: Wave phenomena: analysis and numerics
• Applicant Institution: Karlsruher Institut für Technologie
• Project Heads: Professor Dr. Dirk Hundertmark; Privatdozent Dr. Peer Christian Kunstmann; Professor Dr. Lutz Weis, until 6/2019