How run the code including wiener process function

I understand the code, but I'm not sure what the mistake is or why the Wiener function is causing a problem for me. Did I define something incorrectly? When I remove the Wiener term, the code works, but it must be included.

clc;
clear;

% Parameters
n = 1;
A = 1;                % Amplitude
B = 1;                % Width parameter of soliton
v = 1;                % Velocity of soliton
alpha = 1;            % Nonlinearity parameter
beta = 0.1;           % Dispersion parameter
gamma = 0.05;         % Noise intensity for multiplicative noise

% Grid for xi and time
xi = linspace(-20, 20, 2000);   % Spatial range in transformed coordinates
t = linspace(0, 20, 1000);       % Time range
dt = t(2) - t(1);              % Time step

% Define initial soliton profile (deterministic solution)
u_deterministic = abs(((tanh(0.192e3 ./ 0.35e2 .* t' + xi) - 0.1e1) .^ (0.1e1 ./ 0.4e1)) .* exp(i * (-0.3e1 .* xi - 0.8e1 * t' + (3 .* w(t) ))));

Unrecognized function or variable 'w'.

% Ensure u_deterministic has the correct dimensions (time x space)
if size(u_deterministic, 1) ~= length(t) || size(u_deterministic, 2) ~= length(xi)
    error('Mismatch in dimensions of u_deterministic. Check calculations.');
end

% Initialize storage for the stochastic solution
u_stochastic = zeros(length(t), length(xi));

% Generate Wiener process (increments) for time
W = cumsum(sqrt(dt) * randn(size(t))); % Wiener process for each time step
W = gamma * W; % Scale Wiener process by gamma

% Time evolution
for n = 1:length(t)
    % Apply the Wiener noise factor at time step n
    noise_factor = 1 + W(n);

    % Update solution with multiplicative noise
    u_stochastic(n, :) = u_deterministic(n, :) * noise_factor;
end

% Plot the 3D surface of the stochastic Kudryashov soliton
figure;
surf(xi, t, u_stochastic, 'EdgeColor', 'none');
xlabel('Transformed Space (\xi)');
ylabel('Time (t)');
zlabel('Amplitude (u)');
title('Stochastic Kudryashov Soliton Solution with Multiplicative Noise (Wiener Process)');
colormap jet;
colorbar;

Answer 1

[Cris LaPierre]

You use a function - w(t) - that you do not define in your code. At least that is the error I get in this line:

u_deterministic = abs(((tanh(0.192e3 ./ 0.35e2 .* t' + xi) - 0.1e1) .^ (0.1e1 ./ 0.4e1)) .* exp(i * (-0.3e1 .* xi - 0.8e1 * t' + (3 .* w(t) ))));

Assuming that is the wiener term you are referring to, what is it? It needs to be defined, too.

[salim]

i know where is mistake i want fixed how to plot such graph how w(t) involve to my function the wiener process in stochastic

[Cris LaPierre]

You have already written code for the Wiener process. Can't you just move it up to before you define u_deterministic and then use W' instead of w(t) in your expression?

% Parameters
n = 1;
A = 1;                % Amplitude
B = 1;                % Width parameter of soliton
v = 1;                % Velocity of soliton
alpha = 1;            % Nonlinearity parameter
beta = 0.1;           % Dispersion parameter
gamma = 0.05;         % Noise intensity for multiplicative noise

% Grid for xi and time
xi = linspace(-20, 20, 2000);   % Spatial range in transformed coordinates
t = linspace(0, 20, 1000);       % Time range
dt = t(2) - t(1);              % Time step

% Generate Wiener process (increments) for time
W = cumsum(sqrt(dt) * randn(size(t))); % Wiener process for each time step
W = gamma * W; % Scale Wiener process by gamma

% Define initial soliton profile (deterministic solution)
u_deterministic = abs(((tanh(0.192e3 ./ 0.35e2 .* t' + xi) - 0.1e1) .^ (0.1e1 ./ 0.4e1)) .* exp(i * (-0.3e1 .* xi - 0.8e1 * t' + (3 .* W' ))));

% Ensure u_deterministic has the correct dimensions (time x space)
if size(u_deterministic, 1) ~= length(t) || size(u_deterministic, 2) ~= length(xi)
    error('Mismatch in dimensions of u_deterministic. Check calculations.');
end

% Initialize storage for the stochastic solution
u_stochastic = zeros(length(t), length(xi));



% Time evolution
for n = 1:length(t)
    % Apply the Wiener noise factor at time step n
    noise_factor = 1 + W(n);
    
    % Update solution with multiplicative noise
    u_stochastic(n, :) = u_deterministic(n, :) * noise_factor;
end

% Plot the 3D surface of the stochastic Kudryashov soliton
figure;
surf(xi, t, u_stochastic, 'EdgeColor', 'none');
xlabel('Transformed Space (\xi)');
ylabel('Time (t)');
zlabel('Amplitude (u)');
title('Stochastic Kudryashov Soliton Solution with Multiplicative Noise (Wiener Process)');
colormap jet;
colorbar;

[salim]

Thank you so much! The code isn't mine, actually. I asked the person who sent it to me, but they said they don't remember. Since I'm not very skilled in coding, I decided to ask here for help. I truly appreciate your assistance!

[salim]

@Cris LaPierre can we add below of picture, my mean x direction y-direction and z-direction to if you watch i want see countour of surface what will hapen there is any way to add Z- direction

[salim]

@Cris LaPierre in begin i run don't have issue but now he give me erro which is

Warning: Error updating AxesLayoutManager.

Limits are too large.

Limits are too large.

Limits are too large.

[Cris LaPierre]

Perhaps this post is helpful: https://www.mathworks.com/matlabcentral/answers/457580-limits-are-too-large