Quasi-linear dynamics in nonlinear Schr" odinger equation with periodic boundary conditions

2007/05/28 by M. Burak Erdoğan, Erdogan, M. Burak, Vadim Zharnitsky +1
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Photonic Systems #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.0705.4073

openalex publication_date 2007/05/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is shown that a large subset of initial data with finite energy (L² norm)evolves nearly linearly in nonlinear Schr" odinger equation with periodic boundary conditions. These new solutions are not perturbations of the known ones such as solitons, semiclassical or weakly linear solutions.

Citations

• Invariant Cantor Manifolds of Quasi-Periodic Oscillations for a Nonlinear Schrodinger Equation

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