摘要：In work the new nonlinear mathematical model describing assimilation of the people (population) with some less widespread language by two states with two different widespread languages is offered. In model three subjects are considered: the population and government institutions with the widespread first language, influencing by means of state and administrative resources on the third population with some less widespread language for the purpose of their assimilation; the population and government institutions with the widespread second language, influencing by means of state and administrative resources on the third population with some less widespread language for the purpose of their assimilation; the third population (probably small state education, an autonomy), exposed to bilateral assimilation from two powerful states. In that specific case, a natural zero increase of the population of these three subjects, Cauchy's problem for nonlinear system of the differential equations is solved analytically exactly. Cases of two powerful states assimilating the population of small state education (autonomy), with different number of the population, economic and technological capabilities are considered. The analytical formulas showing in what proportions are received two powerful states assimilate all third population (autonomies). And, conditions under which the first powerful state with the smaller population, than the second powerful state, at the expense of more effective economic and technological capabilities assimilates the most part of the third population (autonomy) are found.
关键词：Nonlinear mathematical model; bilateral assimilation; exact analytical solution; result of assimilation
