File:DS interpenetration swift hohenberg.gif

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

${\displaystyle {\partial }_{t}q=(s_r+i{s}_i){\mathrm{\Delta }}^{2}q+(d_r+i{d}_i)\mathrm{\Delta }q+l_{r}q+(c_r+i{c}_i)|q{|}^{2}q+(q_r+i{q}_i)|q{|}^{4}q.}$

with parameters s_r = -1.0, s_i = 0.0, d_r = -2.0, d_i = 2.0, l_r = -1.7, c_r = 2.5, c_i = 1.0, q_r = -1.0, q_i = 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.

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