Bright-dark solitons and their collisions in mixed<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>N</mml:mi></mml:math>-coupled nonlinear Schrödinger equations

Mixed-type (bright-dark) soliton solutions of the integrable $N$-coupled nonlinear Schr\"odinger (CNLS) equations with mixed signs of focusing- and defocusing-type nonlinearity coefficients are obtained by using Hirota's bilinearization method. Generally, for the mixed $N$-CNLS equations the bright and dark solitons can be split up in $(N\ensuremath{-}1)$ ways. By analyzing the collision dynamics of these coupled bright and dark solitons systematically we point out that for $N&gt;2$, if the bright solitons appear in at least two components, nontrivial effects, such as onset of intensity redistribution, amplitude-dependent phase shift, and change in relative separation distance take place in the bright solitons during collision. However their counterparts, the dark solitons, undergo elastic collision but experience the same amplitude-dependent phase shift as that of bright solitons. Thus, in the mixed CNLS system, there is a coexisting shape-changing collision of bright solitons and elastic collision of dark solitons with amplitude-dependent phase shift, thereby influencing each other mutually in an intricate way.

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