一类具有位势的二维非线性薛定谔系统解的渐近行为

Asymptotic behavior of solutions to nonlinear Schr dinger systems with potentials in 2D

利用质量共振的性质、薛定谔方程的Strichartz估计、薛定谔算子的性质和先验估计的方法,讨论了一类具有位势的二维三次非线性薛定谔系统的小初值问题.证明了该问题整体解的存在性、解的时间衰减估计,并给出了解的长时间渐近行为.

The small initial value problem of a class of two-dimensional cubic nonlinear Schr dinger systems with potential is discussed by using the characters of mass resonance,the Strichartz estimates of Schr dinger equations,the properties of Schr dinger operators and the method of a priori estimates.The existence of the global solution and the time decay estimates of the solution are proved,and the long-time asymptotic behavior of the solution is given.