@Article{JPDE-28-2,
author = {Mohamad, Haidar},
title = {On the Marchenko System and the Long-time Behavior of Multi-soliton Solutions of the One-dimensional Gross-Pitaevskii Equation},
journal = {Journal of Partial Differential Equations},
year = {2015},
volume = {28},
number = {2},
pages = {167--196},
abstract = { 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.},
issn = {2079-732X},
doi = {https://doi.org/10.4208/jpde.v28.n2.6},
url = {https://global-sci.com/article/88276/on-the-marchenko-system-and-the-long-time-behavior-of-multi-soliton-solutions-of-the-one-dimensional-gross-pitaevskii-equation}
}