I have the following two equations:

u=1-(8*(10.3968*t^2-5.8368*t*f-.229376*f^2-5.1984))/(4.56*t^2-2.56*t*f+.8192*f^2+2.28)^2;

x = f+t-(8*(-2.28*t+.64*f))/(2.28+2*(-t+.64*f)^2+2.56*t^2);

How can I plot the contours of u in the x-t plane (with its elevation value labelled in the line of each contour)?

Thank you a lot for your help!

Consider a wave y=f(x,t) with amplitude modulation such that it becomes

 y_new=(1+A)*f(x,t), where A=A(t) is a small perturbation.

How can I do the simulation to test the robustness of the system to see if the wave is stable / unstable under perturbation? As the time t goes to infinity, I want to see if the original wave is distorted or not under either random or prescribed perturbation.

P.S. For example,  f(x,t) = (sech(0.5*x-0.1*t))^2.

Thank you for your help.

I have the following equation:

.9215999996*z^4+.9999999996*z^4*s^4-2.079999999*z^4*s^2-3.212799999*s*z^3+12.63999999*s^3*z^3-7.999999997*s^5*z^3-24.17694443*s^4*z^2-.3071555554*s^2*z^2+23.99999999*s^6*z^2-31.99999999*s^7*z+6.804911108*s^3*z+11.58777777*s^5*z+15.99999999*s^8+5.692222220*s^6-4.853219442*s^4=0

where s is real and z is complex.

How do I plot the graph Im(z) versus s?

Thank you very much for your help!

I have the following two equations:

u=1-(8*(10.3968*t^2-5.8368*t*f-.229376*f^2-5.1984))/(4.56*t^2-2.56*t*f+.8192*f^2+2.28)^2;

x = f+t-(8*(-2.28*t+.64*f))/(2.28+2*(-t+.64*f)^2+2.56*t^2);

How can I plot

(i) a 2-dimensional graph that u versus x at t=0?

(ii) a 3-dimensional graph that u versus x and t ?

Thank you a lot for your help!