Nonlinear peakon PDEs are essential mathematical models in fluid dynamics, which include both the phenomena of soliton interaction and wave breaking. We consider the Cauchy problems for the two-component peakon systems within the project. The peakon systems generalize conventional scalar equations and describe more complex phenomena in the water wave theory. On the other hand, we are interested in the nonlocal (two-place) scalar reductions of these systems, which are related to the nonlocal soliton equations proposed by Ablowitz and Musslimani.
The main goal is to develop the global well-posedness theory and study the blow-up properties of the solutions of the Cauchy problem for the two-component peakon equations. More specifically, we have the following objectives:
- Develop the method of characteristics and obtain the global semigroup of coservative weak solutions of the two-component system on the line
- Introduce the Lipschitz metric for the constructed weak solutions. Thus, obtained semigroup becomes a continuous semigroup with respect to this metric
- Numerically analyze the head-on and over-taking collisions of the two-peakon solutions
Webpage of the prpject https://cordis.europa.eu/project/id/101058830
