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Volume 28, Issue 2
On the Marchenko System and the Long-time Behavior of Multi-soliton Solutions of the One-dimensional Gross-Pitaevskii Equation

Haidar Mohamad

DOI: 10.4208/jpde.v28.n2.6

J. Part. Diff. Eq., 28 (2015), pp. 167-196.

Published online: 2015-06

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  • 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.
  • Keywords

Non-linear Schrödinger equation Gross-Pitaevskii equation

  • AMS Subject Headings

35Q55

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

haidar.mohamad@math.u-psud.fr (Haidar Mohamad)

  • BibTex
  • RIS
  • TXT
@Article{JPDE-28-167, 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 = {http://global-sci.org/intro/article_detail/jpde/5109.html} }
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.
Haidar Mohamad. (2019). On the Marchenko System and the Long-time Behavior of Multi-soliton Solutions of the One-dimensional Gross-Pitaevskii Equation. Journal of Partial Differential Equations. 28 (2). 167-196. doi:10.4208/jpde.v28.n2.6
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