3.4. Approximation Boussinesq

import sympy as sp

tau, xi = sp.symbols('tau xi')
xi

\[\displaystyle \xi\]

psi = sp.Function('psi')(tau,xi)

eq1=psi.diff(tau,2)-psi.diff(xi,2)-sp.diff(3*psi**2+psi.diff(xi,2) , xi,2)
eq1

\[\displaystyle - 6 \psi{\left(\tau,\xi \right)} \frac{\partial^{2}}{\partial \xi^{2}} \psi{\left(\tau,\xi \right)} + \frac{\partial^{2}}{\partial \tau^{2}} \psi{\left(\tau,\xi \right)} - 6 \left(\frac{\partial}{\partial \xi} \psi{\left(\tau,\xi \right)}\right)^{2} - \frac{\partial^{2}}{\partial \xi^{2}} \psi{\left(\tau,\xi \right)} - \frac{\partial^{4}}{\partial \xi^{4}} \psi{\left(\tau,\xi \right)}\]

omega = sp.symbols('omega')
A     = sp.Function('A')
eq1.subs({psi:sp.cos(omega*tau)*A(xi)})

\[\displaystyle - 6 A{\left(\xi \right)} \cos{\left(\omega \tau \right)} \frac{\partial^{2}}{\partial \xi^{2}} A{\left(\xi \right)} \cos{\left(\omega \tau \right)} + \frac{\partial^{2}}{\partial \tau^{2}} A{\left(\xi \right)} \cos{\left(\omega \tau \right)} - 6 \left(\frac{\partial}{\partial \xi} A{\left(\xi \right)} \cos{\left(\omega \tau \right)}\right)^{2} - \frac{\partial^{2}}{\partial \xi^{2}} A{\left(\xi \right)} \cos{\left(\omega \tau \right)} - \frac{\partial^{4}}{\partial \xi^{4}} A{\left(\xi \right)} \cos{\left(\omega \tau \right)}\]

sp.diff?