Formation and Dynamics of Shock Waves in the Degasperis-Procesi Equation

• Autores: H. Lundmark
• Localización: Journal of nonlinear science, ISSN 0938-8974, Vol. 17, Nº 3, 2007, págs. 169-198
• Idioma: alemán
• Texto completo no disponible (Saber más ...)
• Resumen

  • Solutions of the Degasperis-Procesi nonlinear wave equation may develop discontinuities in finite time. As shown by Coclite and Karlsen, there is a uniquely determined entropy weak solution which provides a natural continuation of the solution past such a point. Here we study this phenomenon in detail for solutions involving interacting peakons and antipeakons. We show that a jump discontinuity forms when a peakon collides with an antipeakon, and that the entropy weak solution in this case is described by a "shockpeakon" ansatz reducing the PDE to a system of ODEs for positions, momenta, and shock strengths.