2023/09/07 by Rémi Carles, Carles, Remi
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 #Quantum Mechanics and Non-Hermitian Physics
paper · pdf · doi:10.48550/arxiv.2309.03597
openalex publication_date 2023/09/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the Schrodinger equation with an external potential and a cubic nonlinearity, in the semiclassical limit. The initial data are sums of WKB states, with smooth phases and smooth, compactly supported initial amplitudes, with disjoint supports. We show that like in the linear case, a superposition principle holds on some time interval independent of the semiclassical parameter, in several regimes in term of the size of initial data with respect to the semiclassical parameter. For large data, we invoke properties of compressible Euler equations. For smaller data, we show that there may be no nonlinear interferences on some time interval independent of the semiclassical parameter, and interferences for later time, thanks to explicit computations available for particular phases.