Plotting a function with vectors that show propagation of function.

I want to plot the following fisure with arrows that denote the progation of function.

the valirable is z which goes from to ∞ for the sake of convience I am taking range from -150 to 150.

θ is a function of z which from which we get θ as to .

clear all;
clc;
close all;
z = linspace(-150,150,10000);
pi = 3.1415;
% theta = linspace(-pi/2,pi/2,100);
% z = linspace(-pi/2,pi/2,100);
g2 = 5;
g3 = 0.5;
sigma0 = 0.05;

B = -(3*g2*sigma0-8*g3*sigma0)/((2*g2*sigma0));
D = (3*g2*sigma0-8*g3*sigma0)^2/((6*g2));
u = sqrt(g2*sigma0+2*g3*sigma0);

sigma = sigma0*(1-(B./(1+D.*z.^2)));
theta = -(u*B/(sqrt(1-B)*D)).*atan(sqrt(D./(1-B)).*z);

psi = sqrt(sigma).*(cos(theta)+1i.*sin(theta));

figure(1)
plot3(theta,imag(psi),real(psi));
hold on
plot3(theta, real(psi), zeros(size(theta))-0.5)
plot3(theta, zeros(size(theta))-0.5, imag(psi))
hold off
grid on
xlabel('\theta')
ylabel('Real Part')
zlabel('Imgainary Part')


figure(2)
plot(z,theta);
grid on
xlabel('z')
ylabel('\theta')

the plot I get is this

I want to the plot to look like

I tried using command quiver3(z,theta,imag(psi),real(psi)) but no fruitful results.

What changes will I have to make in my code?

Answer 1

[Alan Stevens]

Does this do what you want:

X = linspace(-150,150,200);

g2 = 5;
g3 = 0.5;
sigma0 = 0.05;

B = -(3*g2*sigma0-8*g3*sigma0)/((2*g2*sigma0));
D = (3*g2*sigma0-8*g3*sigma0)^2/((6*g2));
u = sqrt(g2*sigma0+2*g3*sigma0);

sigma = sigma0*(1-(B./(1+D.*X.^2)));
theta = -(u*B/(sqrt(1-B)*D)).*atan(sqrt(D./(1-B)).*X);

psi = sqrt(sigma).*(cos(theta)+1i.*sin(theta));


Y = zeros(size(X)); Z = zeros(size(X));
U = zeros(size(psi)); V = real(psi); W = imag(psi);
figure(1)
quiver3(X, Y, Z, U, V, W);
axis([-150 150 -20 20 -20 20])