TITLE:
Existence and Stability of Standing Waves for the Nonlinear Schrödinger Equation with Combined Nonlinearities and a Partial Harmonic Potential
AUTHORS:
Wei Wang
KEYWORDS:
Nonlinear Schrödinger Equation, Orbital Stability, Standing Waves
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.12 No.5,
May
10,
2024
ABSTRACT: In this paper, we study the existence of standing waves for the nonlinear Schrödinger equation with combined power-type nonlinearities and a partial harmonic potential. In the L2-supercritical case, we obtain the existence and stability of standing waves. Our results are complements to the results of Carles and Il’yasov’s artical, where orbital stability of standing waves have been studied for the 2D Schrödinger equation with combined nonlinearities and harmonic potential.