We establish a rigorous well-posedness results for the Marchenko system associated to the scattering theory of the one dimensional Gross-Pitaevskii equation （GP）. Under some assumptions on the scattering data, these...We establish a rigorous well-posedness results for the Marchenko system associated to the scattering theory of the one dimensional Gross-Pitaevskii equation （GP）. Under some assumptions on the scattering data, these well-posedness results provide regular solutions for （GP）. We also construct particular solutions, called N- soliton solutions as an approximate superposition of traveling waves. A study for the asymptotic behaviors of such solutions when t-→±∞ is also made.展开更多
文摘We establish a rigorous well-posedness results for the Marchenko system associated to the scattering theory of the one dimensional Gross-Pitaevskii equation （GP）. Under some assumptions on the scattering data, these well-posedness results provide regular solutions for （GP）. We also construct particular solutions, called N- soliton solutions as an approximate superposition of traveling waves. A study for the asymptotic behaviors of such solutions when t-→±∞ is also made.
