Large Time-Stepping Spectral Methods for the Semiclassical Limit of the Defocusing Nonlinear Schrödinger Equation

Figure 1

Numerical solutions for the strong O(1) defocusing nonlinearity by using ED2/EP2. 𝜆=1, 𝜀=0.0025, 𝑁=256. “−“: (𝐴,Δ𝑡)=(0,0.001),(0,0.002), “+ + +", “***": (𝐴,Δ𝑡)=(0.1,0.01),(0.1,0.02). (a) 𝑡=0.5, (b) 𝑡=1.5, (c) 𝑡=10, (d) 𝑡=20.

(a)

(b)

(c)

(d)