| Abstract: |
| In the past few decades in water wave theory, there has been considerable interest in nonlinear dispersive equations that model breaking waves. The best known example is the Camassa-Holm equation, which exhibits wave-breaking behaviour for a large class of initial data and also possesses exact travelling wave solutions having a peak. These solutions, called peakons, are not classical solutions but instead are weak or distributional solutions.
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This talk discusses recent work on a large family of nonlinear dispersive equations that generalize the Camassa-Holm equation and possess single and multi peakon solutions. The nonlinearities in these equations can be much stronger than the nonlinearity in the Camassa-Holm equation, and this has led to finding novel behaviour for 2-peakon interactions (such as bound pairs) as well as generalized peakon solutions (exhibiting acceleration, blow-up, decay, and other behaviour). |
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