Question: How I can separate real and imaginary parts in PDEs ?

Suppose I have a PDE

i*psi[t]+psi[xx] = epsilon*(abs(psi)^2)[yy]*psi:

Here I can set psi = u(x, y, t)+i*v(x, y, t), i = sqrt(-1)

Then my query is, how can I obtain simplified resultant system after equating real and imaginary parts. Of course there would be two partial differential equations in u(x, y, t)and v(x, y, t) and those can also be written down manually very easily but this process becomes difficult when we have large system.

Please help !!!



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