Third-order Boussinesq Lax pair
= Third-order Boussinesq Lax pair
{title2=$L=iD^3-i(qD+Dq)+p,\quad A=3iD^2-4iq$}
The Lax equation $L_t=[L,A]$ for these operators is equivalent to
$$
q_t=3p_x,
\qquad
p_t=q_{xxx}-4(q^2)_x.
$$
Eliminating $p$ gives the <Boussinesq equation>
$$
q_{tt}=3q_{xxxx}-12(q^2)_{xx}.
$$