I am dealing with the integro-differential equation for Wigner function, $$\frac{\partial f}{\partial t}+p\frac{\partial f}{\partial x}+\\+\frac{1}{\chi}\left\{\int_{-\pi}^{+\pi}dy\,\int_{-\infty}^{+\infty}dk\,V(y)f(y,k,t)\right\}\left[f\left(x,p-\frac{\chi}{2},t\right)-f\left(x,p+\frac{\chi}{2},t\right)\right]=0.$$ Here $x$ is the periodic coordinate, $V=V(x)$ is smooth periodic function, and $\chi$ is the positive constant. The function $f=f(x,p,t)$ is the so-called Wigner function and it is periodic, $f(x,p,t)=f(x+2\pi,p,t)$. My goal is to implement numerical solution of this equation for known initial conditions.
My knowledge in numerical solutions is quite poor, so it is not to easy to do it myself. However, I know that the numerical investigation of Wigner equation is intensively studied. I assume that some realizations in Python already exist, but I cannot find something suitable for me.
After revising some papers, I suppose that operator splitting method will work for my problem. So,
My question: Do some Python packages/modules for numerical solution of Wigner equation exist?
