Hello, I am trying to use FEniCsX to solve a time-dependent PDE with a non-linear coefficient. However, I am getting an error stating: “ValueError: Found Argument in Cos id=6262508512, this is an invalid expression.” …when I formulate my variational problem `(a,L)=system(F)`

. I am wondering if this is because system() sets up a linear system to solve with a linear solver? Also can NonLinearSolver() be used to solve time-dependent PDEs? My PDE is essentially a Fokker-plank equation with a non-linear drift (or velocity) term. Please find my code below. Any help/clarification would be greatly appreciated. Thanks in advance!

```
import numpy as np
import matplotlib
import matplotlib.pyplot as plt
from dolfinx import mesh, fem, io, plot, la
import pyvista
import ufl
import numpy as np
from dolfinx import *
import dolfinx
import numpy, sys
from mpi4py import MPI
from petsc4py import PETSc
from ufl import (VectorElement, FiniteElement,
SpatialCoordinate, TrialFunction, TestFunction,
as_vector, cos, sin, inner, div, grad, dx, pi, system)
from dolfinx import mesh, fem, io, nls, log
from dolfinx.fem.petsc import NonlinearProblem
from dolfinx.nls.petsc import NewtonSolver
##cretae a rectangular mesh with quadrilateral elements
##note: here theta=x
from mpi4py import MPI
length, height = 10, 3
Nx, Ny = 80, 60
extent = [[0., 0.], [length, height]]
domain = mesh.create_rectangle(
MPI.COMM_WORLD, extent, [Nx, Ny], mesh.CellType.quadrilateral)
##define the non-linear coeff
omega=(np.pi/2)
##define the non-linear coefficient
def vel(x):
return omega + cos(x)
##setting up the variational problem
from ufl import (TestFunction, SpatialCoordinate, TrialFunction,
as_vector, dx, grad, inner, system, equation, Constant)
V = fem.FunctionSpace(domain, ("Lagrange", 1))
u = TrialFunction(V) ##time-dep c at n+1
v = TestFunction(V)
un = fem.Function(V) ##time dep C at n
D= fem.Constant(domain, 1.0) ##diffusion constant
dt = fem.Constant(domain, 0.05)
##define the variational problem
F= (un*v*ufl.dx) - (v*ufl.dx) ##note: i think it should be L=un*v -v*dx
F-= u*dx - v*dx - vel(u)*u*v*dt*dx - D*dt*inner(grad(u), grad(v))*dx + D*dt*v*dx
#variational problem stated as a=L
(a,L)=system(F)```
```