2013/07/22 by Hans Lindblad, Avy Soffer, Lindblad, Hans +1
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Photonic Systems #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.1307.5882
openalex publication_date 2013/07/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the 1D Klein-Gordon equation with variable coefficient cubic\nnonlinearity. This problem exhibits a striking resonant interaction between the\nspatial frequencies of the nonlinear coefficients and the temporal oscillations\nof the solutions. In the case where the worst of this resonant behavior is\nabsent, we prove L-Infinity scattering as well as a certain kind of strong\nsmoothness for the solution at time-like infinity with the help of several new\nnormal-forms transformations. Some explicit examples are also given which\nsuggest qualitatively different behavior in the case where the strongest cubic\nresonances are present.\n