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arXiv · 1501.06033

On the Marchenko system and the long-time behavior of multi-soliton solutions of the one-dimensional Gross-Pitaevskii equation

Haidar Mohamad
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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 $N-$soliton solutions as an approximate superposition of traveling waves. A study for the asymptotic behaviors of such solutions when $t\rightarrow\pm \infty$ is also made.

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Haidar Mohamad. 2015-01-24. On the Marchenko system and the long-time behavior of multi-soliton solutions of the one-dimensional Gross-Pitaevskii equation. https://arxiv.org/abs/1501.06033

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