I have a third order derivative of a variable, say U, which is a function of both space and time. du/dx * du/dx * du/dt or (d^3(U)/(dt*dx^2)) The Fourier transform of du/dx is simply ik*F(u) where F(u) is the Fourier transform of u. The Fourier transform of d^2(u)/(dx^2) is simply -(k^2)*F(u) where F(u) is again the Fourier transform of u. My question is, how do handle the time derivative part with a Laplace transform? What would the Fourier-Laplace transform of the given PDE look like?