I have the following 5th degree Polynomial Equation in **complex wave velocity** w(tauT, tauq) as a function of real parameters taoT and tauq:
   

    eqn = (1 + (c2^2/c1^2)*w^2)*(1 + k*taoT*c2*w + (c2*d/k)*w*(1 + k*tauq*c2*w + (1/2)*k^2*tauq^2*c2^2*w^2)) + (e*c2*d/k)*w*(1 + k*tauq*c2*w + (1/2)*k^2*tauq^2*c2^2*w^2) == 0;

The parameters are given as:

    c1=4631.0; c2=2280.1; d=8066.8; e=0.0168; k=1; 

The range for both of taoT and Taoq is: 

    [10^-10, 10^-1]

Some authors' have plotted the following graphs from the above equations. I don't know Mathematica very well but need some help for my research.
[![enter image description here][1]][1]


Also, **marked the extremum values and points** if possible on both the graphs.
Can anyone please help me for plotting like above two figures? I am in basic level in learning Mathematica 11.0. Seeking kind help!

Thank you very much.


    

   

    


  [1]: https://i.sstatic.net/fb8Vw.jpg