Abstract
Different integrable discretizations of AB system are proposed in this paper. Discrete AB (dAB) system and two different versions of semi-discrete AB (sdAB) systems are obtained by discretization of associated Lax pair of continuous integrable AB system. Discrete multiple soliton solutions are constructed for dAB system and sdAB systems by applying Darboux transformation. In order to explain our construction we also computed discrete single and double soliton solutions for dAB and sdAB systems. Dynamics of one discrete bright and dark soliton solution and interaction of two discrete bright-bright and dark-dark soliton solutions for dAB system have been presented.
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