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I want to solve these differential equations and want to get the value of 'a1'. I used this code given below but it is not showing any result. If anyone can resolve this will be appreciated.

wm = 1;
G1 = 0.005;
delc = 1;
ka = 0.1;
E0 = 0.4;
gma1 = 0.5;
g0 = 1;
kd = 0.2;
del0 = 1;
N1 = 1;
NDSolve[{q1'[t] - wm*p1[t] == 0, 
 p1'[t] + wm*q1[t] - G1*Abs[a1[t]]^2 + gma1*p1[t] == 0, 
 a1'[t] + (I*delc + ka)*a1[t] - I*G1*a1[t]*q1[t] - E0 + I*g0*s1[t] == 
 0, s1'[t] + (kd - I*del0/2*N1)*s1[t] - I*g0*a1[t]*N1 == 0, 
q1[0] == 0, p1[0] == 0, a1[0] == 1, s1[0] == 0}, {q1, p1, a1, 
s1}, {t, 0, 100}]
Show[a1[t]]

here 'Abs' is used for, dagger of a[t] multiply with a[t].

Improve this question
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    $\begingroup$ Have you looked at the error messages? NDSolve::underdet "There are more dependent variables, {a1[t],p1[t],q[t],q1[t],s1[t]}, \ than equations, so the system is underdetermined" $\endgroup$
    – Nasser
    Commented Apr 6, 2020 at 4:21
  • $\begingroup$ @Nasser Many have solved these types of equations numerically. Should I separate these equations in the imaginary and real terms and then after solve? $\endgroup$
    – vini
    Commented Apr 6, 2020 at 4:30
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    $\begingroup$ Possibly, yes, but first, I would worry about having more dependent variables than equations than worry about the complex part. Is having more dependent variables than equations intentional? $\endgroup$
    – Nasser
    Commented Apr 6, 2020 at 4:32
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    $\begingroup$ One of your DE's has the varible q[t]. Maybe it should be q1[t] ? $\endgroup$
    – LouisB
    Commented Apr 6, 2020 at 4:36
  • $\begingroup$ @LouisB yes you are right. Now I need the value of 'a1'. how can i get it? $\endgroup$
    – vini
    Commented Apr 6, 2020 at 7:44

1 Answer 1

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An easy way to plot the real and imaginary parts of the solution for a1[t is like this

soln = NDSolve[{q1'[t] - wm*p1[t] == 0,
    p1'[t] + wm*q1[t] - G1*Abs[a1[t]]^2 + gma1*p1[t] == 0, 
    a1'[t] + (I*delc + ka)*a1[t] - I*G1*a1[t]*q1[t] - E0 + 
      I*g0*s1[t] == 0, 
    s1'[t] + (kd - I*del0/2*N1)*s1[t] - I*g0*a1[t]*N1 == 0,
    q1[0] == 0, p1[0] == 0, a1[0] == 1, s1[0] == 0}, {q1, p1, a1, 
    s1}, {t, 0, 100}];

ReImPlot[a1[t] /. soln, {t, 0, 15}]

enter image description here

To create a similar plot with Mathematica 9 we can code

Plot[Evaluate[{Re@a1[t], Im@a1[t]} /. soln], {t, 0, 15},
 PlotStyle -> {Automatic, Dashed}]

The latest Mathematica features, however, are available with a basic Wolfram Cloud account (free).

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  • $\begingroup$ Thankyou. It is helpful. $\endgroup$
    – vini
    Commented Apr 6, 2020 at 12:38
  • $\begingroup$ But I am using Mathematica version 9.0 . The plot is not shown. $\endgroup$
    – vini
    Commented Apr 6, 2020 at 12:53

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