2017/06/17 by Zhong Han, Yong Chen
Physics and Astronomy · #nlin.SI
paper · pdf · doi:10.1515/zna-2017-0133
arXiv admin note: substantial text overlap with arXiv:1706.05498
arxiv created 2017/06/17 · arxiv updated 2017/09/13
By virtue of the KP hierarchy reduction technique, we construct the general bright-dark mixed N-soliton solution to the multi-component Mel'nikov system comprised of multiple (say M) short-wave components and one long-wave component with all possible combinations of nonlinearities including all-positive, all-negative and mixed types. Firstly, the two-bright-one-dark (2-b-1-d) and one-bright-two-dark (1-b-2-d) mixed N-soliton solutions in short-wave components of the three-component Mel'nikov system are derived in detail. Then we extend our analysis to the M-component Mel'nikov system to obtain its general mixed N-soliton solution. The formula obtained unifies the all-bright, all-dark and bright-dark mixed N-soliton solutions. For the collision of two solitons, the asymptotic analysis shows that for a M-component Mel'nikov system with M ≥ 3, inelastic collision takes place, resulting in energy exchange among the short-wave components supporting bright solitons only if the bright solitons appear at least in two short-wave components. Whereas, the dark solitons in the short-wave components and the bright solitons in the long-wave component always undergo elastic collision which just accompanied by a position shift.