Improved Lower Bound for the Radius of Analyticity of Solutions to the Fifth Order, KdV-BBM Type Equation

We show that the uniform radius of spatial analyticity \(\sigma (t)\) $\sigma (t)$ of solutions at time t to the fifth order, KdV-BBM type equation cannot decay faster than \(1/ \sqrt{t}\) $1/\sqrt{t}$ for large t, given initial data that is analytic with fixed radius \(\sigma _0\) ${\sigma }_0$ . This improves a recent result by Belayneh, Tegegn and the third author [2], where they obtained a 1/t decay of \(\sigma (t)\) $\sigma (t)$ for large time t.