File:DS interpenetration swift hohenberg.gif

Summary
Space time plot of two colliding dissipative solitons in the complex Swift-Hohenberg equation, generated by Dr. Hendrik U. Boedeker(June 2007).

The system used was


 * $$ \partial_t q = (s_r+ i s_i) \Delta^2 q + (d_r+ i d_i) \Delta q + l_r q + (c_r + i

c_i)|q|^2 q + (q_r + i q_i) |q|^4 q.$$

with parameters sr = -1.0, si = 0.0, dr = -2.0, di = 2.0, lr = -1.7, cr = 2.5, ci = 1.0, qr = -1.0, qi = 0.0, no-flux boundary conditions. The initial phase difference between the dissipative solitons is 0, but the qualitative outcome in the same for other phase differences as well. A finite element code was used for the simulation.