Bump On Tail

using VlasovSolvers
using Plots
using LaTeXStrings

dev = CPU()                  # device
stepper = StrangSplitting()  # timestepper
dt = 0.1                     # timestep
nsteps = 1000                # total number of time-steps

α   = 0.03
kx  = 0.3

n1, n2 = 32, 64
x1min, x1max = 0.0, 2π / kx
x2min, x2max = -9., 9.

mesh1 = OneDGrid(dev, n1, x1min, x1max)
mesh2 = OneDGrid(dev, n2, x2min, x2max)

f = DistributionFunction( mesh1, mesh2 )


for (i,x) in enumerate(mesh1.points), (j,v) in enumerate(mesh2.points)
    f.values[i,j]  = (1.0+α*cos(kx*x)) / (10*sqrt(2π)) * (9*exp(-0.5*v^2)+2*exp(-2*(v-4.5)^2))
end


nsteps = 500
t   = range(0.0, stop=50.0, length=nsteps)
dt  = t[2]

prob = VlasovProblem(f, BSLSpline(5), dev)

sol = solve(prob, stepper, dt, nsteps )

plot(sol, yscale = :log10, label=L"\sqrt{\int e^2dx}")