Solution
= Solution
Differentiating
$$
L=-\frac d{dx}\,p^2\frac d{dx}
$$
with respect to time gives
$$
L_t=-\frac d{dx}\left(2pp_t\frac d{dx}\right).
$$
If $p_t=p^3p_{xxx}$, then
$$
L_t=-\frac d{dx}\left(2p^4p_{xxx}\frac d{dx}\right)=LA-AL.
$$
\b[Thus $L_t=[L,A]$ is an <Isospectral Lax equation>, and $(L,A)$ is a <Lax pair> for the <Harry Dym equation>.]