4 papers
Asymptotic behavior of mass-critical Schrödinger equation in
Fanfei Meng, Yilin Song, Ruixiao Zhang
In this paper, we study the long-time behavior for the mass-critical nonlinear Schrödinger equation on the line \[ i\partial_t u + \partial_x^2 u = |u|^4 u, u(0, x) = u_0 \in L_x^2…
On Growth of Sobolev norms for cubic Schrödinger equation with harmonic potential in dimensions
Yilin Song, Ruixiao Zhang, Jiqiang Zheng
In this article, we study the growth of higher-order Sobolev norms for solutions to the defocusing cubic nonlinear Schrödinger equation with harmonic potential in dimensions $d=2,3…
Global well-posedness for the defocusing cubic nonlinear Schrödinger equation on
Yilin Song, Ruixiao Zhang
In this article, we investigate the global well-posedness for the defocusing, cubic nonlinear Schrödinger equation posed on $\T^3$ with intial data lying in its critical space $H^\…
On scattering for two-dimensional quintic Schrödinger equation under partial harmonic confinement
Zuyu Ma, Yilin Song, Ruixiao Zhang +2
In this article, we study the scattering theory for the two dimensional defocusing quintic nonlinear Schrödinger equation(NLS) with partial harmonic oscillator which is given by \b…