Consider the following modified GL equation: where the unknown function u(x, t)
ID: 2983084 • Letter: C
Question
Consider the following modified GL equation: where the unknown function u(x, t) = u1(x, t) + iu2(x, t) is a complex - valued function, |u|2 = u 2/1 + u 2/2 and i = -1. The parameters rho i(i = 0,1, 2) are real numbers and rho is the system parameter. Answer the following questions: Rewrite the equation (2) as a system of two equations in terms of u1 and u2 (see (4)). Rewrite the system from that you derived in the problem (i) as a system of tau which satisfies a special conditions u"1 = -u1 and u"2 = - u2 (see (6)). Use the polar coordinates to derive equations in terms of the amplitude r( tau ) and the phase 0 (see (7)).Explanation / Answer
wait , it is complex