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The term non-linear or nonlinear has several definitions but is generally used to describe a system that cannot be approximated by a superposition principle or perturbative approach.
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Mixing for Burgers equation in 2+1D
Let us consider the following (2+1)-dimensional Burgers-like equation:
$$
u_t + (u^2)_x + (u^3)_y=0.
$$
Here the unknown is a function $u= u(t,x,y):(0,\infty) \times \mathbb R^2 \to \mathbb R$.
Is the …