In [1]:

    

%pylab inline

# JSAnimation import available at https://github.com/jakevdp/JSAnimation
from JSAnimation import IPython_display
from matplotlib import animation


    

    




Populating the interactive namespace from numpy and matplotlib

In [2]:

    

def wave(x,t,k0,c,sigmak,pkmax,nstep):
    total=0
    dk=2*pkmax*sigmak/nstep
    for i in range(nstep):
        k=k0 - pkmax *sigmak+i*dk
        omega=c*k
        total += exp(-(k-k0)**2/sigmak)*exp(1j*(k*x-omega*t))*dk
        # print (i,'k=',k)
    return (total.real)


    

In [3]:

    

#     k0,c,sigmak,pkmax,nstep
params=[1, .2, 0.1, 5, 20]


    

In [4]:

    

wave(2.7, 10, *params)


    

    
Out[4]:





0.41415166898140243

In [13]:

    

k0=1
sigmak=0.02*k0
c=0.1
pkmax=5
kstep=10

xx=10
xmin=-xx*2*pi/k0
xmax=xx*2*pi/k0
xstep=300

nstep=20

params=[k0,c,sigmak,pkmax,nstep]
ymax=wave(0, 0, k0, c,sigmak, pkmax, kstep)


    

In [14]:

    

x = np.linspace(xmin, xmax, xstep)
y=wave(x, 0, k0, c,sigmak, pkmax, kstep)

print('ymax =',ymax)
plot(x,y)


    

    




ymax = 0.170719983921






    
Out[14]:





[<matplotlib.lines.Line2D at 0x7f382afc2198>]






    

In [12]:

    

%%capture
# create a simple animation
fig = plt.figure()

ax = plt.axes(xlim=(xmin,xmax), ylim=(-ymax, ymax))
line, = ax.plot([], [], lw=2)

def init():
    line.set_data([], [])
    return line,

def animate(i):
    line.set_data(x, wave(x, i,*params))
    return line,


    

In [19]:

    

animation.FuncAnimation(fig, animate, init_func=init,
                        frames=linspace(-700,700,120),interval=20, blit=True)


    

    
Out[19]:








    
    

    
    

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     Once 
     Loop 
     Reflect 
  

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