Study of solutions of singularly perturbed equations by splitting and replacing initial conditions with varying initial conditions

In this paper, a singularly perturbed equation (SPE) of the first order is considered. The main task is to split the solution of the given equation into several (finite) components, so that each component is dominant in different parts of the considered complex region and simplifies the conducted research. To facilitate the conducted research, the initial conditions are replaced by variable initial conditions on some lines.