Nonlinear maps preserving the polynomial

Let $\mathbb F$ be a field and $P \in \mathbb F [x_1,\ldots, x_n]$ be a homogeneous polynomial such that $|\mathbb F| > °(P)$ and $ϕ, ψ\colon \mathbb F^n \to \mathbb F^n$ be two maps such that $P(\mathbf{x} + λ\mathbf{y}) = P(ϕ(\mathbf{x}) + λψ(\mathbf{y}))$ for all $λ\in \mathbb F$ and $\mathbf{x},