On the existence of special solutions of the generalized Davey-Stewartson system
Applied Mathematics Letters, cilt.22, sa.8, ss.1174-1177, 2009 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 22 Sayı: 8
- Basım Tarihi: 2009
- Doi Numarası: 10.1016/j.aml.2008.09.003
- Dergi Adı: Applied Mathematics Letters
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.1174-1177
- Anahtar Kelimeler: GDS system, Pohozaev type identity, Travelling waves
- Boğaziçi Üniversitesi Adresli: Evet
Özet
In this note we show that for certain choice of parameters the hyperbolic-elliptic-elliptic generalized Davey-Stewartson system admits time-dependent travelling wave solutions of the kind given in [V.A. Arkadiev, A.K. Pogrebkov, M.C. Polivanov, Inverse scattering transform method and soliton solutions for Davey-Stewartson II equation, Physica D 36 (1989) 189-197] for the hyperbolic Davey-Stewartson system. These solutions lead to radial solutions as well. We also find the sufficient conditions for non-existence of travelling wave solutions for the hyperbolic-elliptic-elliptic generalized Davey-Stewartson system by using the point of view developed in [A. Eden, T.B. Gürel, E. Kuz, Focusing and defocusing cases of the purely elliptic generalized Davey-Stewartson system, IMA J. Appl. Math. (in press)]. © 2009 Elsevier Ltd. All rights reserved.