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- #1

u_t + u_{xxx} + 6uu_x &= 0\\

L &= \partial_{xx} + u_t\\

M &= -4\partial_{xxx} - 3(2u\partial_x + u_x)

\end{align}

For the \(L\) operator, should that be \(u\) not \(u_t\)?

I ask because I found

\begin{align}

\partial_{xx}\psi &= (\lambda - u)\psi\\

\partial_t\psi &= (-4\partial_{xxx} - 6u\partial_x - 3u_x)\psi

\end{align}

Also, where did \(\lambda\) come from?