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Orbital stability of the black soliton to the Gross-Pitaevskii equation

Béthuel, Fabrice; Gravejat, Philippe; Saut, Jean-Claude; Smets, Didier (2008), Orbital stability of the black soliton to the Gross-Pitaevskii equation, Indiana University Mathematics Journal, 57, 6, p. 2611-2642. http://dx.doi.org/10.1512/iumj.2008.57.3632

Type
Article accepté pour publication ou publié
External document link
http://hal.archives-ouvertes.fr/hal-00270348/en/
Date
2008
Journal name
Indiana University Mathematics Journal
Volume
57
Number
6
Pages
2611-2642
Publication identifier
Metadata
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Author(s)
Béthuel, Fabrice
Gravejat, Philippe
Saut, Jean-Claude
Smets, Didier
Abstract (EN)
We establish the orbital stability of the black soliton, or kink solution, $\v_0(x) = \th \big( \frac{x}{\sqrt{2}} \big)$, to the one-dimensional Gross-Pitaevskii equation, with respect to perturbations in the energy space.
Subjects / Keywords
Gross-Pitaevskii equation; kink solution; black soliton; orbital stability