Smoothing of a class of fifth order model evolution equations. (English) Zbl 0839.35123

Tom, Michael M.

Differ. Integral Equ. 9, No. 1, 45-58 (1996).

Summary: 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 KdV equation.

MSC:

35Q53	KdV equations (Korteweg-de Vries equations)
35B65	Smoothness and regularity of solutions to PDEs
35Q51	Soliton equations

Keywords:

fifth-order evolution equations; Sawada-Kotera equation; Kaup equation; Korteweg-de Vries equation; solitary-wave solutions