In Ginzburg Landau equation, there is a term,
$ |A|^2A$
and $A$ is space and time dependent function or $A(x,t)$ Why do we have norm or absolute value under square? Is square not enough? My guess is that if we have a complex variable say $ A =-a+ib$ then according to the above we should get $(a^2 + 2ib-b^2)(-a+ib)$. Without the norm, the results will be different. Am I correct?
Seems like you're wrong, suppose $$ A = -a + bi $$ then $$ |A| = \sqrt{a^2 + b^2} $$ $$ |A|^2 = |A||A| = \sqrt{a^2 + b^2} * \sqrt{a^2 + b^2} = a^2 + b^2 $$ and $$ |A|^2 A = (a^2 + b^2)(-a + bi) = -a(a^2 + b^2) + b(a^2 + b^2)i $$ I think the purpose is to get rid of the square