Homoclinic Structure for a Generalized Davey-Stewartson System

Babaoglu, Ceni; Hacinliyan, Irma

doi:10.1007/978-3-319-30379-6_3

Ceni Babaoglu⁷ &
Irma Hacinliyan⁷

1748 Accesses

Abstract

In this study, we analyze the homoclinic structure for the generalized Davey-Stewartson system with periodic boundary conditions. This system involves three coupled nonlinear equations and describes (2 + 1) dimensional wave propagation in a bulk medium composed of an elastic material with coupled stresses. We first provide linearized stability analysis of the plane wave solutions of the generalized Davey-Stewartson system. Then, give an analytic description of the characteristics of homoclinic orbits near the fixed point by finding soliton type solutions. These solutions are derived via Hirota’s bilinear method. We also show that two of these solutions form a pair of symmetric homoclinic orbits and all these symmetric homoclinic orbit pairs construct the homoclinic tubes.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Chapter: USD 29.95; Price excludes VAT (USA)

eBook: USD 169.00; Price excludes VAT (USA)

Softcover Book: USD 219.99; Price excludes VAT (USA)

Hardcover Book: USD 219.99; Price excludes VAT (USA)

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

Ablowitz, M.J., Herbst, B.M.: On homoclinic structure and numerically induced chaos for the nonlinear Schrodinger equation. SIAM J. Appl. Math. 50, 339–351 (1990)
Article MathSciNet MATH Google Scholar
Babaoglu, C., Erbay, S.: Two-dimensional wave packets in an elastic solid with couple stresses. Int. J. Non-Linear Mech. 39, 941–949 (2004)
Article MATH Google Scholar
Babaoglu, C., Eden, A., Erbay, S.: Global existence and nonexistence results for a generalized Davey-Stewartson system. J. Phys. A Math. Gen. 37, 11531–11546 (2004)
Article MathSciNet MATH Google Scholar

Download references

Author information

Authors and Affiliations

Faculty of Science and Letters, Department of Mathematics, Istanbul Technical University, 34469, Maslak-Istanbul, Turkey
Ceni Babaoglu & Irma Hacinliyan

Authors

Ceni Babaoglu
View author publications
You can also search for this author in PubMed Google Scholar
Irma Hacinliyan
View author publications
You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ceni Babaoglu .

Editor information

Editors and Affiliations

Department of Mathematics and Statistics, University of Montreal, Montreal, Québec, Canada
Jacques Bélair
Department of Mathematics, University of British Columbia, Vancouver, British Columbia, Canada
Ian A. Frigaard
Department of Mathematics and Statistics, University of Guelph, Guelph, Ontario, Canada
Herb Kunze
Department of Mathematics, Wilfrid Laurier University, Waterloo, Ontario, Canada
Roman Makarov
MS2Discovery Institute, Wilfrid Laurier University, Waterloo, Ontario, Canada
Roderick Melnik
Department of Computer Science, University of Saskatchewan, Saskatoon, Saskatchewan, Canada
Raymond J. Spiteri

Rights and permissions

Reprints and permissions

Copyright information

About this paper

Cite this paper

Babaoglu, C., Hacinliyan, I. (2016). Homoclinic Structure for a Generalized Davey-Stewartson System. In: Bélair, J., Frigaard, I., Kunze, H., Makarov, R., Melnik, R., Spiteri, R. (eds) Mathematical and Computational Approaches in Advancing Modern Science and Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-30379-6_3

Download citation

DOI: https://doi.org/10.1007/978-3-319-30379-6_3
Published: 11 August 2016
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-30377-2
Online ISBN: 978-3-319-30379-6
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)

Publish with us

Policies and ethics