  By using the Darboux transformation, we obtain two new types of
exponential-and-rational mixed soliton solutions for the defocusing nonlocal
nonlinear Schrodinger equation. We reveal that the first type of solution can
display a large variety of interactions among two exponential solitons and two
rational solitons, in which the standard elastic interaction properties are
preserved and each soliton could be either the dark or antidark type. By
developing the asymptotic analysis technique, we also find that the second type
of solution can exhibit the elastic interactions among four mixed asymptotic
solitons. But in sharp contrast to the common solitons, the asymptotic mixed
solitons have the t-dependent velocities and their phase shifts before and
after interaction also grow with |t| in the logarithmical manner. In addition,
we discuss the degenerate cases for such two types of mixed soliton solutions
when the four-soliton interaction reduces to a three-soliton or two-soliton
interaction.
