Multiple-scale analysis: Difference between revisions

Revision as of 07:18, 18 August 2014

Revision as of 01:07, 13 October 2014

Line 74:

:<math>Y_0(t,t_1) = A(t_1)\, e^{+it} + A^\ast(t_1)\, e^{-it},</math>

with ''A''(''t''₁) a [[complex number|complex-valued]] [[amplitude]] to the zeroth-order solution ''Y''₀(''t'',&nbsp;''t''₁) and ''i''²&nbsp;=&nbsp;−1. Now, in the first-order problem the forcing in the [[right hand side]] of the differential equation is

:<math>\left[ -3\, A^2\, A^\ast - 2\, i\, \frac{dA}{dt_1} \right]\, e^{+it} - A^3\, e^{+3it} + c.c.</math>