TY - JOUR
T1 - On the Marchenko System and the Long-time Behavior of Multi-soliton Solutions of the One-dimensional Gross-Pitaevskii Equation
AU - Mohamad , Haidar
JO - Journal of Partial Differential Equations
VL - 2
SP - 167
EP - 196
PY - 2015
DA - 2015/06
SN - 28
DO - http://doi.org/10.4208/jpde.v28.n2.6
UR - https://global-sci.org/intro/article_detail/jpde/5109.html
KW - Non-linear Schrödinger equation
KW - Gross-Pitaevskii equation
AB -  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 Nsoliton solutions as an approximate superposition of traveling waves. A study for the asymptotic behaviors of such solutions when t → ± ∞ is also made.