clear all; close all

% 1D nonlinear Schrodinger equation
%
%   i u_t + 1/2 u_xx + |u|^2 u = 0
%
L=20; n=128; tspan=0:1:10;
x2=linspace(-L/2,L/2,n+1); x=x2(1:n);
k=(2*pi/L)*[0:n/2-1 -n/2:-1];

u=sech(x);
ut=fft(u);

[t,utsol]=ode45('rhs1',tspan,ut,[],k);
for j=1:length(t)
    usol(:,j)=ifft( utsol(j,:).' );
end
figure(1), surf(t,x,abs(usol));
figure(2), surfl(t,x,abs(usol));
figure(3), surfc(t,x,abs(usol));
figure(4), mesh(t,x,abs(usol));
figure(5), waterfall(x,t,abs(usol'));


% 2D coupled nonlinear heat equation
%
%   u_t = u_xx + u_yy + v^2
%   v_t = v_xx + v_yy + u^2
%
Lx=20; nx=64; Ly=20; ny=64; tspan2=[0:0.1:1];
x2=linspace(-Lx/2,Lx/2,nx+1); x=x2(1:nx);
y2=linspace(-Ly/2,Ly/2,ny+1); y=y2(1:ny);
kx=(2*pi/Lx)*[0:nx/2-1 -nx/2:-1];
ky=(2*pi/Ly)*[0:ny/2-1 -ny/2:-1];

[X,Y]=meshgrid(x,y);
[KX,KY]=meshgrid(kx,ky);
kx2=reshape(KX,nx*ny,1); ky2=reshape(KY,nx*ny,1);

u=exp(-X.^2-Y.^2); v=exp(-X.^2-Y.^2);
ut=fft2(u); vt=fft2(v);
ut2=reshape(ut,nx*ny,1); vt2=reshape(vt,nx*ny,1);
uvt=[ut2; vt2];

[t,uvtsol]=ode45('rhs2',tspan2,uvt,[],kx2,kx2,ny,ny);

for j=1:9
  u2t=uvtsol(j,1:nx*ny); v2t=uvtsol(j,nx*ny+1:2*nx*ny);  
  u=ifft2( reshape(u2t,nx,ny) );
  v=ifft2( reshape(v2t,nx,ny) );
  figure(6), subplot(3,3,j), surf(real(u))
  figure(7), subplot(3,3,j), surf(real(v))
end