Skip Navigation


IMA Journal of Applied Mathematics Advance Access originally published online on December 17, 2004
IMA Journal of Applied Mathematics 2005 70(1):15-24; doi:10.1093/imamat/hxh050
This Article
Right arrow Full Text (PDF)
Right arrow All Versions of this Article:
70/1/15    most recent
hxh050v1
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Similar articles in ISI Web of Science
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrow Search for citing articles in:
ISI Web of Science (2)
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Eden, A.
Right arrow Articles by Erbay, S.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

IMA Journal of Applied Mathematics Vol. 70 No. 1 © Institute of Mathematics and its Applications 2005; all rights reserved.

On travelling wave solutions of a generalized Davey–Stewartson system*

Alp Eden1 § and Saadet Erbay2 ¶

1 Department of Mathematics, Bogazici University, 34342 Bebek, Istanbul, Turkey, 2 Department of Mathematics, Isik University, 34398 Maslak, Istanbul, Turkey  §

The generalized Davey–Stewartson (GDS) equations, as derived by Babaoglu & Erbay (2004, Int. J. Non-Linear Mech., 39, 941–949), is a system of three coupled equations in (2 + 1) dimensions modelling wave propagation in an infinite elastic medium. The physical parameters ({gamma}, m1, m2, {lambda} and n) of the system allow one to classify the equations as elliptic–elliptic–elliptic (EEE), elliptic–elliptic–hyperbolic (EEH), elliptic–hyperbolic–hyperbolic (EHH), hyperbolic–elliptic–elliptic (HEE), hyperbolic–hyperbolic–hyperbolic (HHH) and hyperbolic–elliptic–hyperbolic (HEH) (Babaoglu et al., 2004, preprint). In this note, we only consider the EEE and HEE cases and seek travelling wave solutions to GDS systems. By deriving Pohozaev-type identities we establish some necessary conditions on the parameters for the existence of travelling waves, when solutions satisfy some integrability conditions. Using the explicit solutions given in Babaoglu & Erbay (2004) we also show that the parameter constraints must be weaker in the absence of such integrability conditions.

Keywords: Davey–Stewartson equations; nonlinear Schrödinger equation; Pohozaev identity; radial solutions; travelling wave.

* Dedicated to Ray W. Ogden on the occasion of his 60th birthday

§ Email: eden{at}boun.edu.tr

Email: serbay{at}isikun.edu.tr


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer: Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.