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| The Degasperis-Procesi equation (DP) is one of several equations known to model important nonlinear effects such as wave breaking and shock creation.
What is quite unique about the DP equation is that these two effects can be studied in an
explicit way with the help of the multipeakon ansatz. In essence, one is presented with the
view of wave breaking as a collision of hypothetical particles (peakons and antipeakons).
I will show that the system of ODEs describing DP multipeakons has the Painlev\'{e} property which leads to a universal wave breaking behaviour. Other interesting features are:
(i) multipeakons can collide only in pairs;
(ii) there are no multiple collisions other than, possibly simultaneous, collisions of peakon-antipeakon pairs at different locations;
(iii) each peakon-antipeakon collision results in creation of a shock thus making possible a multi-shock phenomenon.
This is joint work with Lingjun Zhou (Tongji University, Shanghai, P.R. China). |
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