How plot 2D and 3D of a function with contain wiener process?

I have a function that includes a Wiener process, which I am encountering for the first time in a solution. I want to plot this function but am unsure how to proceed, as I have no experience plotting such functions

(sech(0.288e3 / 0.143e3 * t + x) ^ (0.1e1 / 0.4e1)) * exp(i * (-0.3e1 * x - 0.3e1 * t + (2 * W(t))))

Answer 1

[Sameer]

Hi @salim saeed

The Wiener process can be simulated using random walks.

Here's an example of how you can plot your function:

% Parameters
t_max = 20; % Maximum time
x_max = 20; % Maximum space
dt = 0.01; % Time step
dx = 0.1; % Space step

% Time and space vectors
t = 0:dt:t_max;
x = -x_max:dx:x_max;

% Initialize Wiener process
W = zeros(size(t));
for i = 2:length(t)
    W(i) = W(i-1) + sqrt(dt) * randn; % Random walk
end

% Preallocate solution matrix
U = zeros(length(x), length(t));

% Calculate the function
for i = 1:length(x)
    for j = 1:length(t)
        U(i, j) = (sech(0.288e3 / 0.143e3 * t(j) + x(i)) ^ (0.1e1 / 0.4e1)) * ...
            exp(1i * (-0.3e1 * x(i) - 0.3e1 * t(j) + (2 * W(j))));
    end
end

% Plot the real part of the solution
figure;
surf(t, x, real(U));
shading interp;
xlabel('Time (t)');
ylabel('Transformed Space (\xi)');
zlabel('Amplitude (u)');
title('Stochastic Kudryashov Soliton Solution with Multiplicative Noise (Wiener Process)');
colorbar;

Hope this helps!

[salim]

thank you for your help but i have some issue with graph the quality og graph is not suatable for publishing in journals How i can get a beter view of my graph like in below picture