2024/03/05 by Masaki Kawamoto, Kawamoto, Masaki, Hayato Miyazaki +1 · 1 citation
Mathematics · #Advanced Mathematical Physics Problems #Spectral Theory in Mathematical Physics #Numerical methods in inverse problems
paper · doi:10.48550/arxiv.2403.02657
This paper is concerned with nonlinear Schrödinger equations with a time-decaying harmonic potential. The nonlinearity is gauge-invariant of the long-range critical order. In [24] and [22], it is proved that the equation admits a nontrivial solution that behaves like a free solution with a logarithmic phase correction in the frameworks of both the final state problem and the initial value problem. Furthermore, a modified scattering operator has been established in the case without the potential in [15]. In this paper, we construct a modified scattering operator for our equation by utilizing a generator of the Galilean transformation. Moreover, we remove a restriction for the coefficient of the potential which is required in [22].