How to plot solutions for different values of parameters on same file?

How to plot solutions for different values of parameters on same file i..e,

close all;

X=-5:.1:5;

T=-5:.1:5;

%i=1;

w0=.5;

%h=3;

eta=(1./2);

sig=-1;

e0=2*w0*sqrt(eta-sig);

mu1=.5*1i;

[x,t]=meshgrid(X,T);

%a=4*mu1.^2-(w0.^2./2);

A=(1./(-2*w0.^2+2*mu1.^2)*sqrt(e0.^2-4*mu1.^2).*((-2*w0.^2+2*mu1.^2)*x+t));

a=e0*sinh(A)-2*1i*mu1;

b=e0+2*1i*mu1*sinh(A);

r1=e0-4*1i*mu1*(a./b);

surf(x,t,abs(r1));

shading flat;

grid off;

How to plot 'r1' for different values of 'mu1' on same figure like this

Answer 1

[Vedant Shah]

Hi @Wajahat,

To plot solutions for different values of a parameter on the same figure, the ‘hold’ function in MATLAB can be utilized. By looping through various values of ‘mu1’, calculating ‘r1’ for each, and plotting the corresponding surface using the ‘surf’ function, it is possible to visualize multiple solutions simultaneously. Assigning distinct colours to each surface and adding a legend increases the interpretability of the plot.

The following sample code demonstrates this approach:

mu1_list = [0.5i, 1i, 1.5i]; 

figure; 
hold on;  

colors = lines(length(mu1_list));  

for k = 1:length(mu1_list) 
    mu1 = mu1_list(k); 
    A = (1./(-2*w0.^2 + 2*mu1.^2) * sqrt(e0.^2 - 4*mu1.^2) .* ((-2*w0.^2 + 2*mu1.^2)*x + t)); 
    a = e0 * sinh(A) - 2*1i*mu1; 
    b = e0 + 2*1i*mu1 * sinh(A); 
    r1 = e0 - 4*1i*mu1 * (a ./ b); 
    surf(x, t, abs(r1), 'FaceAlpha', 0.6, 'EdgeColor', 'none', 'FaceColor', colors(k,:)); 
end 

shading flat; 
grid off; 
xlabel('x'); 
ylabel('t'); 
zlabel('|r_1|'); 
title('Solutions for different values of \mu_1'); 
legend(arrayfun(@(m) sprintf('\\mu_1 = %.1fi', imag(m)), mu1_list, 'UniformOutput', false)); 
hold off; 

The result obtained using the above sample code is as follows:

The resulting figure displays the surfaces corresponding to different values of ‘mu_1’ on the same axes, each distinguished by a unique colour and identified in the legend.

For further information, refer to the following documentations:

• https://www.mathworks.com/help/matlab/ref/hold.html
• https://www.mathworks.com/help/matlab/ref/legend.html