BoundaryValueDiffEq: How to restart to exploit initial guess?

Specific Domains
1

My boundary value problem has a parameter that renders the problem easy or hard.

Is there a way to restart the solve function for the hard problem by specifying the solution of the easy problem as initial guess?

Below a MWE (solves Burgers equation by harmonic balancing. If nonlinscaling=0 (see below), problem reduces to linear Helmholtz equation)

# set source function 
src(x) = 1. 

# set right-hand side 
function rhs!(du, u, p, x)
    c, omd = p
    C = u[1]; A = u[2]; B = u[3]
    dC = du[1]; dA = du[2]; dB = du[3]
    nonlinscaling = 0.2
    du[1] = nonlinscaling*(A*dA+B*dB+C*dC)
    du[2] = omd/c*B + nonlinscaling*(A*dC+C*dA) 
    du[3] = -omd/c*A - src(x)/c + nonlinscaling*(B*dC+C*dB) 
end

# set boundary conditions 
function bc(residual, u, p, x)
    Cleft = 0; Aleft = 0; Bleft=0; 
    residual[1] = u[1][1] - Cleft
    residual[2] = u[1][2] - Aleft 
    residual[3] = u[1][3] - Bleft 
end

# set constants 
c = 0.2
omd = 2*pi
p = [c, omd]

# set domain size 
xspan = (0.,1.)

# set initial guess 
start = [0., 1., 1.]

# define and solve the problem 
bvp = BVProblem(rhs!, bc, start, xspan,p)
sol = solve(bvp, MIRK4(), dt = 0.005)