| Abstract: |
| In 2013, Ablowitz and Musslimani first proposed an integrable nonlocal nonlinear Schrodinger (NNLS) model. By using the two-fold Darboux transformation, we obtain two families of mixed exponential and rational soliton solutions for the NNLS model. It is revealed that the first family of solutions can display a large variety of interactions among two exponential solitons and two rational solitons, in which the elastic soliton interaction properties are preserved and each soliton could be either the dark or anti-dark type. By developing the asymptotic analysis technique, we also find that the second family of solutions can exhibit the elastic interactions among four mixed solitons. But in sharp contrast to the common solitons, the mixed solitons have the $t$-dependent velocities and the phase shift of the interacting solitons before and after interaction grows with $|t|$ in the logarithmical manner. In addition, we discuss the degenerate cases when the four-soliton interaction reduces to a three-soliton or two-soliton interaction. |
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