%
%  code07.m -- steepest descent (djm, 01 oct 01)
%

z = [9 -9];
for j=1:2
  zz = z(j);

%  parameters
  Lx = 5.0;  Ly = 5.0;  Nx = 50;  Ny = 50;

%  coordinates
  x = -Lx:Lx/Nx:Lx;  y = -Ly:Ly/Ny:Ly;

%  2D coordinates 
  [xg,yg] = meshgrid(x,y);  kg = xg + i*yg;

%  exponents

  iphi = i* ((kg.^3)/3 + zz*kg);

%  steepest descent quantities
 
  k_sd = sqrt(-zz);  iphi_sd = i*k_sd * (2*zz/3);

%  2D plots

  figure(j);  clf;  colormap(copper)
  pcolor(x,y,real(iphi));  shading flat;  cbar
  hold on;  axis square
  cont = max([abs(real(iphi_sd)) abs(imag(iphi_sd))]);
  contour(x,y,real(iphi),cont*[-3:3],'w-');
  contour(x,y,imag(iphi),cont*[-3:3],'w:');
  xlabel('\bf real(k)')
  ylabel('\bf imag(k)')
  title(['\bf Airy steepest descent curves (dotted):  z=' num2str(zz)])
end
