%
%  guide.m -- (djm:  26 feb 2004)
%    - phase plane for waveguide
%

%  phase plane coordinates
xp = -pi/2:pi/200:pi/2;
x = -pi:pi/100:pi;

[xg,xpg] = meshgrid(x,xp);

%  first integral
a = 0.5;
yg = 2*(1+sech(xg).^2) - xpg.^2;

%  plot
figure(1);  clf

%  critical contour & non-propagating traj
contour(x,xp,yg,'k');  
hold on
contour(x,xp,yg,[1 1]*3,'r');  

title('\bf single waveguide phase plane')
xlabel('\bf x-axis')
ylabel('\bf x''-axis')