A new phenomenon of the formation of a solitary population wave of insects (Zygogramma suturalis, Chrysomelidae) appearing on introduction into a free ecological niche has been discovered. During dispersion of the insects over the new territory as a result of the purposive search by them for food (Ambrosia artemisiifolia) a solitary sustained density wave of the insects appears moving at constant speed and characterized by complete destruction of the weed after its passage. To describe this phenomenon a new simple mathematical model is proposed differing both from known models of autowaves and soliton-like models.