Multi-component semi-discrete coupled dispersionless integrable system, its lax pair and Darboux transformation

Lax pair representations of multi-component semi-discrete coupled dispersionless (sdCD) integrable system have been presented. A Lax pair is derived for the multi-component sdCD system in the form of a block matrices through generalizing the 2 × 2 Lax pair matrices to the case of 2N × 2N. A Darboux transformation is studied for the multi-component sdCD system and is used to compute soliton solutions of the system.