Higher-order hybrid-pattern solitons on the $n$-periodic background for the reverse-space-time derivative nonlinear Schr\"{o}dinger equation.

The Darboux transformation formulae for the reverse-space-time derivative nonlinear Schr\"{o}dinger equation are given by using concise expressions. At the same time, the $n$-solitons, $n$-periodic solutions, higher-order hybrid-pattern solitons and some mixed solutions are obtained through Darboux transformation formulae. It's worth mentioning that the solution of reverse-space-time DNLS equation can be reduced to the solution of local DNLS equation by symmetry relation. In the case of zero seed solution, the fact that solution $q[N]$ at origin depends only on the spectral parameters is proved. Also, the amplitudes of $n$-solitons, $n$-periodic solutions, higher-order solitons and mixed solutions are derived. Moreover, many interesting new phenomena are discovered through detailed dynamic analysis of these solutions. For example, interactions of $n$-periodic waves produce peaks with different amplitudes and size. Soliton on the periodic background looks very similar to breathers due to the interception of the periodic background. Finally, the modulational instability analysis for the reverse-space-time derivative nonlinear Schr\"{o}dinger equation is studied. The results are useful for describing the interaction process of solitons interference by $n$-periodic waves in the ocean and other fields.