Abstract
We present a non–commutative extension of two-component complex coupled integrable disspersionless (NC-CCID) system. We studied matrix Darboux transformation and generate multiple soliton solutions by using the notation of quasideterminants. Further, we obtain single and double soliton solutions in terms of quasideterminants for NC-CCID system. In the commutative limit, we obtain soliton solutions for CCID system as ratio of ordinary determinants.
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