A RANDOM DISPERSION SCHRODINGER EQUATION WITH NONLINEAR TIME-DEPENDENT LOSS/GAIN

作者：Jian, Hui^*; Liu, Bin

来源：Bulletin of the Korean Mathematical Society, 2017, 54(4): 1195-1219.

DOI：10.4134/BKMS.b160330

• nonlinear Schrodinger equation
• random dispersion
• time-dependent nonlinear loss/gain
• nonlinear fibre optics

In this paper, the limit behavior of solution for the Schrodinger equation with random dispersion and time-dependent nonlinear loss/gain: idu + 1/epsilon m (t/epsilon(2))partial derivative(xx) udt + vertical bar u vertical bar(2 sigma) udt + i epsilon a(t)vertical bar u vertical bar(2 sigma 0) udt = 0 is studied. Combining stochastic Strichartz-type estimates with L-2 norm estimates, we first derive the global existence for L-2 and H-1 solution of the stochastic Schrodinger equation with white noise dispersion and time-dependent loss/gain: idu + Delta u circle d beta + vertical bar u vertical bar(2 sigma) udt + ia(t)vertical bar u vertical bar(2 sigma 0) udt = 0. Secondly, we prove rigorously the global diffusion-approximation limit of the solution for the former as epsilon -> 0 in one-dimensional L-2 subcritical and critical cases.

• 出版日期2017-7
• 单位华中科技大学