Hey Jazz
I understand that you would like to visualize the critical points through the Korteweg-de Vries (KDV) equation coefficients. For this, firstly the “critical condition” has to be defined in the context of the problem.
For instance, a critical condition might be when the real part of A (referring to your code) crosses a specific threshold or changes sign. For this critical condition, here’s how your code can be modified to plot the critical condition points.
critical_Y = [];
critical_A_real = [];
threshold = 0; % critical condition (Assuming zero crossing)
for i = 1:length(Y)
A = (a + b_- 2 * y2) / (c + d);
A_real = real(A);
% Checking the critical condition
if abs(A_real - threshold) < 1e-3 % Tolerance
critical_Y = [critical_Y, Y(i)];
critical_A_real = [critical_A_real, A_real];
end
end
Finally, the critical points can be plotted as follows.
plot(critical_Y, critical_A_real, 'ro');
Ensure that the critical condition definition aligns with the theoretical understanding of the problem. Adjust the threshold and tolerance as needed to capture the relevant points.
I hope this helps.
