An interference head wave (Buldyrev's wave) and localization principle

In the series of articles V. S. Buldyrev was considering interference head waves. We will call these waves as Buldyrev waves. Our main goal is to obtain formulas describing Buldyrev's wave using localization principle. Similar formulas were deduced (from another but also heuristic considerations) by V. S. Buldyrev earlier. Different point of view on a Buldyrev's wave was proposed by V. M. Babich. Some formulas for the waves of this class contain an illusory contradiction with concept of localization. We demonstrate that the contradiction is fictitious and formulas deduced by V. S. Buldyrev and results obtained later agree with localization principle.