<p>We illustrate the concept of asymptotic integrability of nonlinear wave equations, which is understood as integrability of the dynamics of wave packets propagating over a large-scale background, using the generalized Korteweg–de Vries equation as an example. It is shown that the asymptotic integrability condition naturally leads to the generalized Bohr–Sommerfeld rule, which determines the parameters of the asymptotic solitons born from an intense initial pulse. The additional assumption that the Bohr–Sommerfeld rule is a quasiclassical limit for a certain linear spectral problem allows us to single out a class of completely integrable equations, find the corresponding Lax pair, and estimate the accuracy of the Bohr–Sommerfeld rule for nonintegrable equations.</p>