clear all

N=2*256;
Lx=2*pi;
xE=linspace(0,2*pi,N+1);
x=xE(1:N);

P=[0:N/2-1,-N/2:-1];
Ps=fftshift(P);
Kx=2*pi/Lx*P;

OM=sign(Kx).*sqrt(abs(Kx));

xc=Lx/4;a=0.4;
kc=Kx(42);

cg=1/2/sqrt(kc);


0.1/cg

dt=0.2;


f=exp(-(x-xc).^2/a^2).*cos(kc*x);


fhat=fft(f);
fn=real(ifft(fhat));

figure(6)
plot(P,fhat.*conj(fhat),'+k','markersize',18)
set(gca,'fontsize',24)



Nt=600;

for it=1:Nt
    t=(it-1)*dt;
    fthat=fhat.*exp(-1i*OM*t);
    ft=real(ifft(fthat));
    fen=exp(-(x-xc-cg*t).^2/a^2);

figure(5)
plot(x,ft,'b',x,fen,'--r','linewidth',2,'markersize',18)
set(gca,'fontsize',24)
drawnow
%pause(0.2)
end