Smoothing of a class of fifth order model evolution equations

Abstract

Solutions of a class of fifth-order model evolution equations corresponding to initial data in relatively weak function spaces are shown to exhibit a smoothing effect of the type of Kato. These models include the next hierarchy of the Korteweg-de Vries equation. It is interesting to observe that conditions that guarantee smoother solutions in some of these weaker function spaces are exactly the ones that allow for the equation to admit solitary-wave solutions of the characteristic $\text{sech}^{2}$ profile of the K-dV equation.