% load the data
>> load KdV.mat

% here is a solution of the initial value problem with soliton initial data.
% note that the solution rigidly translates, as expected.
>> figure(1)
>> clf
>>for j=1:31, plot(x,u2(:,j)); axis([0,2*pi,0,150]); pause(1); end

% here, I gave the solition initial data to two equations.  First, I gave
% it to the KdV equation and computed a solution.  Then I gave it to the
% Airy equation (u_t + u_xxx = 0) and computed a solution.  In the following
% I plot the solutions at equal times.  Note the effect of dispersion.
>> figure(2)
>> clf
>> for j=1:31, plot(x,u2(:,j)); hold on; plot(x,U2(:,j)); axis([0,2*pi,-50,150]); hold off; pause(1); end

% Here, I took as initial data the sum of two soliton profiles with a short
% fat soliton in front of a tall thin soliton.  This initial data was given
% to the KdV code.  Note the soliton interaction. 
>> figure(3)
>> clf
>> for j=1:31, plot(x,u3(:,j)); axis([0,2*pi,0,150]); pause(1); end

% Here, I plot the above solution, while also plotting in red what the 
% solitons would've done in the absence of any interaction.  Note that 
% the tall, thin solition is advanced as a result of the interaction and
% the short, fat soliton is retarded.
>> figure(4)
>> clf
>> for j=1:31, plot(x,u3(:,j)); hold on; plot(x,u1(:,j),'r'); plot(x,u2(:,j),'r'); axis([0,2*pi,0,150]); hold off; pause(1); end