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In this talk,we are concerned with a focusing and defocusing complex short pulse equation(CSPE).Similar to the NLS equation,the focusing CSPE admits bright soliton solution,while the defocusing CSPE possessing dark soliton solution.Through a reduction from 2DTL hierarchy and Hirota's bilinear method,multi-soliton solutions of both bright type and dark type are constructed for focusing and defocusing complex short pulse equation,respectively.