ON THE STABILITY OF THE COMPACTON WAVES FOR THE DEGENERATE KDV AND NLS MODELS
Küçük Resim Yok
Tarih
2022
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Brown Univ
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
In this paper, we consider the degenerate semi-linear Schrodinger and Korteweg-de Vries equations in one spatial dimension. We construct special solutions of the two models, namely standing wave solutions of NLS and traveling waves, which turn out to have compact support, compactons. We show that the compactons are unique bellshaped solutions of the corresponding PDEs and for appropriate variational problems as well. We provide a complete spectral characterization of such waves, for all values of p. Namely, we show that all waves are spectrally stable for 2 < p <= 8, while a single mode instability occurs for p > 8. This extends previous work of Germain, Harrop-Griffiths and Marzuola [Quart. Appl. Math. 78 (2020), pp. 1-32] who have previously established orbital stability for some specific waves, in the range p < 8.
Açıklama
Anahtar Kelimeler
Standing Waves, Solitary Waves, Existence, Equations, Solitons
Kaynak
Quarterly Of Applied Mathematics
WoS Q Değeri
Q4
Scopus Q Değeri
Q2
Cilt
80
Sayı
3
