2021/12/13 by Satoshi Masaki, Masaki, Satoshi, Jun‐ichi Segata +3
Mathematics · Physics and Astronomy · #35B40 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Photonic Systems #Numerical methods for differential equations #Primary 35Q55 #Secondary 35A22
paper · pdf · doi:10.48550/arxiv.2112.06427
openalex publication_date 2021/12/13 · openalex created_date 2021/12/31 · openalex updated_date 2026/07/28
In this paper, we consider the large time asymptotic behavior of solutions to systems of two cubic nonlinear Schr"odinger equations in one space dimension. It turns out that for a system there exists a small solution of which asymptotic profile is a sum of two parts oscillating in a different way. This kind of behavior seems new. Further, several examples of systems which admit solution with several types of behavior such as modified scattering, nonlinear amplification, and nonlinear dissipation, are given. We also extend our previous classification result of nonlinear cubic systems.