function solInt(choice) 

%choice = 0 or 1. 
%0 for far off solitons moving towards each other. 
%1 for stationary, but overlapping solitons.
%plots solitons in time, with x-t plot, and image plot.

% variable parameters.........
if choice == 0
    x0 = 3;         %soliton displacement
    T = .3;         %time duration
    dt = .00003;    %time step
    k = 10;         %wave number
else
    x0 = 1;
    T = 1.3;
    dt = .0001;
    k = 0;
end
%............................
      
% set parameters ..........
xmin = -10;
xmax = 10;
n = 150;            %lattice points
c = 2;              %width and height of soliton. note: must match non-linearity strength, B.
B = -2;             %non-linear strength. 
% .................

dx = (xmax-xmin)/n;    %spatial step
x = xmin + (1:n)'*dx;  %x is col vec   

a = -1/(dx)^2;
b = 1/(2*dx^2);

% creation of K the sparse matrix
D = sparse(1:n,1:n,a,n,n);
E = sparse(2:n,1:n-1,b*ones(1,n-1),n,n);
K = E+D+E';

U = c*sech(c*(x-x0)).*exp(-1i*k*x) + c*sech(-c*(x+x0)).*exp(1i*k*x);
I = speye(n,n);           % keeps everything sparse 
t = 0;

%using CN scheme in paper...
Uold = U;
Unew = zeros(n,1);
modT = 100;
xtU = zeros(n,(T + modT*dt)/(modT*dt));     %records U as time goes on

while t < T
  if (mod(floor(t/dt),modT)==0)
    xtU(:,floor(t/(modT*dt) + 1)) = U.*conj(U);
    plot(x, [U.*conj(U) real(U) imag(U)]); 
    axis([xmin xmax -1 15]);
    text(1,1, sprintf('t=%g, prob=%g', t, dx*dot(U,U)));
    drawnow;
  end
    Unew = (I - 1i*dt*K)\((I + 1i*dt*K)*U - B*1i*dt*(3/2*conj(U).*U.*U - 1/2*conj(Uold).*Uold.*Uold));
    Uold = U;
    U = Unew;
    t = t + dt;
end


figure;
surf(xtU);
colorbar;

if choice == 0
    text(50,100,25,'seperated soliton collision');
else
    text(75,100,25,'overlapping solitons');
end
    
    figure;
    imagesc(xtU');
    set(gca,'ydir','normal');
    colorbar;