File:DS interpenetration swift hohenberg.gif

Summary[edit]

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

${\displaystyle \partial _{t}q=(s_{r}+is_{i})\Delta ^{2}q+(d_{r}+id_{i})\Delta q+l_{r}q+(c_{r}+ic_{i})|q|^{2}q+(q_{r}+iq_{i})|q|^{4}q.}$

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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