Spekaker
Magnus C. Ørke, University of Oslo
Abstract
In recent years global bifurcation theory in combination with precise regularity estimates has been used to prove existence of specific classes of traveling wave solutions for nonlinear and nonlocal PDEs. I will discuss this method for a class of fractional Korteweg–De Vries and fractional Degasperis–Procesi equations with an inhomogeneous Fourier multiplier of parametrized order in the range of (-1, 0), and show that there are highest, cusped traveling-wave solutions for both equations, characterized by optimal Hölder regularity exactly attained in the cusp.