Darboux transformation and soliton solutions of the spatial discrete coupled complex short pulse equation

This paper aims to constructing the Darboux transformation and soliton solutions of the focusing and defocusing spatial discrete coupled complex short pulse (sd-CCSP) equation. With the Darboux transformation, we derived three types of soliton solutions for the focusing sd-CCSP equation, which include smooth-, cuspon-and loop-type. These solutions converge to exact solutions for the focusing CCSP equation in the continuum limit. The interaction of two solitons and their asymptotic behavior are analyzed. We also obtain three types of soliton solutions for the defocusing sd-CCSP equation, as well as the rational solutions for the focusing sd-CCSP equation. We find that there exist new properties of soliton solutions for the sd-CCSP equation which do not exist in the sd-CSP equation, and there is a big difference between sd-CCSP equation and spatial discrete coupled nonlinear Schrodinger (sd-CNLS) equation. (C) 2022 Published by Elsevier B.V.