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Solving an integro differential equation involving hilbert transform

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Mohan Aditya Sabbineni
Please help me in solving this integro differential equation. I am unable write a code for this.
∂f/∂t−(H(f)(∂f/∂x)=0
where [H(f)] is hilbert transform of 'f.'
and f=f(x,t) and initial condition is f(x,0)=cos(x) and also has periodic boundary conditions given by F{H{f(x′,t)}}=i⋅sgn(k)F{f(x,t)}, where F(f(x,t) is fourier transform of f(x,t).
and here ''t'' runs from 0 to 1.3 seconds
so I think we have to use iterations on basis of 't' while solving this equation.
And suggestions are highly appreciated.

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