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

Figure 3

Numerical solutions of Example 5.1 by ED2/EP2 for the weak 𝑂(𝜀) defocusing nonlinearity (𝜀=0.01). (a) Position density 𝜌 at 𝑡=0.5 (before breaking), at 𝑡=1.5 (after breaking), at 𝑡=10. (b) Current density 𝐽 at 𝑡=0.5 (before breaking), at 𝑡=1.5 (after breaking), at 𝑡=10. (c) Evolution of the position density 𝜌 (left) and the current density 𝐽 (right).

(a)

(b)

(c)