On the question of soft capture in differential games with several pursuing and a single evading player

For a differential game with several pursuers and a single evader the paper gives a way of constructing approach strategies that separates to a sufficient degree the role of inertialess actions from inertial actions in the system of differential equations. Controlled differential systems with additive right-hand side can be carried over by a change of variables to a form making it possible to formulate a certain decomposed differential game with several players. The part of this new game relating to the inertialess actions is called a generalized simple pursuit. It is proved that the original game and the decomposed game are equivalent in the sense of the existence of approach strategies. Two classical examples are considered for inertial objects with the same dynamical possibilities, sufficient conditions are found for soft l-capture, and exact soft approach is shown to be impossible.