Folds, bosonization and non-triviality of the classical limit of 2D string theory

In the 1-dimensional matrix model one identifies the tachyon field in the asymptotic region with a nonlocal transfom of the density of fermions. But there is a problem in relating the classical tachyon field with the surface profile of the Fermi fluid if a fold forms in the Fermi surface. Besides the collective field additional variables W_j(x) are required to desrcibe folds. In the quantum theory we show that the W_j are the quantum dispersions of the collective field. These dispersions become O(1) rather than O(h) precisely after fold formation, thus giving additional "classical" quantities and leading to a rather nontrivial classical limit. A coherent pulse reflecting from the potential wall turns into high energy incoherent quanta (if a fold forms), the frequency amplification being of the order of the square root of the number of quanta in the incident wave.