Mathematics – Analysis of PDEs
Scientific paper
2009-03-27
Communications in Partial Differential Equations 35, 1 (2010) 113-164
Mathematics
Analysis of PDEs
Final version accepted for publication in Communications in Partial Differential Equations with a few minor corrections and ad
Scientific paper
10.1080/03605300903222542
In this paper, we proceed along our analysis of the Korteweg-de Vries approximation of the Gross-Pitaevskii equation initiated in a previous paper. At the long-wave limit, we establish that solutions of small amplitude to the one-dimensional Gross-Pitaevskii equation split into two waves with opposite constant speeds $\pm \sqrt{2}$, each of which are solutions to a Korteweg-de Vries equation. We also compute an estimate of the error term which is somewhat optimal as long as travelling waves are considered. At the cost of higher regularity of the initial data, this improves our previous estimate.
Bethuel Fabrice
Gravejat Philippe
Saut Jean-Claude
Smets Didier
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