| 概要 | We consider the initial value problem
for the fifth order modified KdV equation.
We show the existence of the local solution
which is real analytic in both time and space variables,
if the initial data $\phi\in H^{s}(\R)$ $(s\geq 3/4)$
satisfies the condition
\begin{eqnarray*} \sum_{k=0}^{\infty}
\frac{\large{A_0^k}}{\large{k!}}{\|}(x\pt_x)^k\phi{\|}_{H^s}<{\infty},
\end{eqnarray*}
for some constant $0<A_0<1$.
The proof of our main result is based
on the contraction principle and the bootstrap argument.
In this talk we will present an outline of the proof for this result. |