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In this paper, we obtain the coupled bright-bright and the coupled dark-dark soliton solutions for an integrable coupled semidiscrete Hirota equation (ICDHE) using the bilinear method. These solutions have both singular and nonsingular behaviors depending upon the choice of the parameters. The distinguishing feature of the ICDHE is that the singular solution can possess some nonsingular characteristics in the discrete space at some time. The asymptotic behavior of these coupled bright-bright and the coupled dark-dark solitons is studied in order to explain their collision properties

Solitons and dynamic properties of the coupled semidiscrete Hirota equation