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Some Analytical Results for Equations with Nonlinear Dispersion

PDE and Applied Math Seminar

Speaker: David Ambrose, Drexel University
Location: 1147 MSB
Start time: Tue, May 11 2010, 4:12PM

Solutions of equations with nonlinear dispersion exhibit very different behaviors from solutions of equations with linear dispersion. The most well-known family of equations with nonlinear dispersion is probably the Rosenau-Hyman compacton equations; while some exact solutions, especially compactly supported traveling waves, are known, there is as yet no analytical theory for these equations. We will present existence results for some equations with nonlinear dispersion which are similar to the Rosenau-Hyman equations, and we will exhibit compactly supported traveling waves for the same equations. Additionally, positivity-preserving properties and conserved quantities will be discussed. This is joint work with J. Douglas Wright.