Abstract
According to the new nonlocal integrable reduction proposed by Ablowitz and Musslimani, we study the complex shifted reverse space-time modified Korteweg-de Vries equation. The soliton, the kink-type breather and higher-order rogue waves solutions are constructed by using the Darboux transformation method. The effects of the spectral parameter and space-time shift parameters on the solution are discussed respectively, and the dynamic behavior of them is described from the expression and image of the solution. In addition, by comparing with the standard PT symmetry, we discuss the new structure of different solutions due to the space-time shift parameters.
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