H4-Solutions for the Olver–Benney equation

Abstract

The Olver–Benney equation is a nonlinear fifth-order equation, which describes the interaction effects between short and long waves. In this paper, we prove the global existence of solutions of the Cauchy problem associated with this equation.

On classical solutions for the fifth‐order short pulse equation

“…In particular, integrating () on (0, t ), by (), we have (). Finally, since () holds, arguing as in Coclite and di Ruvo, 62 (Lemma 3.2) we obtain () and ().…”