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I need to evaluate the following derivate:

$$\frac{dF}{d\Psi} = \frac{d}{d\Psi}\left[\beta\Delta\Psi+\alpha\left|\Psi\right|^2\Psi+\mu\Psi-i\vec{v}\cdot\bar{\nabla}\Psi\right]$$

where $\Psi$ is a complex eigenfunction $\Psi(x,y,t)$. In particular I am not sure on how to evaluate the derivate when there is also the Laplacian of Psi and the gradient. Any suggestion?

Paul T.
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StrizzenSuperfluid
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  • Ps. I am doing this numerically, so actually I don't know the shape of Psi. I only need to know how to evaluate this derivate with respect of Psi, so that I can then execute it numercally in a Fortran code. – StrizzenSuperfluid May 09 '22 at 10:14
  • You can find the answer here: https://physics.stackexchange.com/questions/109518/derivation-of-euler-lagrange-equations-for-lagrangian-with-dependence-on-second – Hossein May 09 '22 at 13:04

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