Question: How complex solution satisfy a PDE( involving Conjugate).

with(PDEtools):
V:=-exp(I*(k*x+omega*t+theta))*sqrt((k^2+omega)/(k*sigma))*sech(sqrt(k^2+omega)*(-2*k*t+x));
pde[1] := simplify(I*(diff(V, t, t))+diff(V, x, x)-I*sigma*V*(conjugate(V)*(diff(V, x))-V*(diff(conjugate(V), x)))) = 0;

 

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