I'm trying to substitute some dependent variables into equations inside of a matrix, however $Replace[]$ and and $/.$ don't seem to work.
The equation in question is just a vector matrix of differential equations, which I eventually intend to solve.
NTISE =
{
{((-(Ωc2^2 - I*γ*Ωo1))*a[t] + Ωd2^2*b[t] + 2*I*Ωo1*Derivative[1][a][t])/Ωo1},
{(Ωd2^2*a[t] + (Ωc2^2 + I*γ*Ωo1)*b[t] + 2*I*Ωo1*Derivative[1][b][t])/Ωo1},
{((-Ωc2^2 + 2*Ωe^2 + I*γ*Ωo2)*c[t] + Ωd2^2*d[t] + 2*I*Ωo2*Derivative[1][c][t])/Ωo2},
{(Ωd2^2*c[t] + (Ωc2^2 + 2*Ωe^2 + I*γ*Ωo2)*d[t] + 2*I*Ωo2*Derivative[1][d][t])/Ωo2}
}
And the expressions I would like to substitute in are
ΔΩ1 = Ωc2^2/Ωo1
ΔΩ2 = Ωc2^2/Ωo2
ωd1 = Ωd2^2/Ωo1
ωd2 = Ωd2^2/Ωo2
These expressions should simplify the DEs above in order to get equations that can then be solved, however, I tried using
NTISE /.
{ Ωc2^2/Ωo1 -> ΔΩ1,
Ωc2^2/Ωo2 -> ΔΩ2,
Ωd2^2/Ωo1 -> ωd1,
Ωd2^2/Ωo2 -> ωd2}
To no avail, and furthermore attempted
Replace[NTISE,
{ Ωc2^2/Ωo1 -> ΔΩ1,
Ωc2^2/Ωo2 -> ΔΩ2,
Ωd2^2/Ωo1 -> ωd1,
Ωd2^2/Ωo2 -> ωd2}, Infinity]
And got the same equations out.
NTISE /. {\[CapitalOmega]c2^2 -> \[CapitalDelta]\[CapitalOmega]1, \ \[CapitalOmega]c2^2 -> \ \[CapitalDelta]\[CapitalOmega]2*\[CapitalOmega]o2, \ \[CapitalOmega]d2^2 -> \[Omega]d1*\[CapitalOmega]o1, \ \[CapitalOmega]d2^2 -> \[Omega]d2*\[CapitalOmega]o2} // Simplify
$\endgroup$ – Jānis Šmits Jul 18 '18 at 19:22a*b->c
would replace instances of a*b in the expression before theReplaceAll
which has a shorthand/.
. Then I changed your replacement rules by multiplying both sides by the denominator. Instead of\[CapitalOmega]c2^2/\[CapitalOmega]o1 -> \[CapitalDelta]\ \[CapitalOmega]1
I wrote\[CapitalOmega]c2^2 -> \ \[CapitalDelta]\[CapitalOmega]1*\[CapitalOmega]o1
$\endgroup$ – Jānis Šmits Jul 18 '18 at 20:19