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Homoclinic Structure for a Generalized Davey-Stewartson System

In: Mathematical and Computational Approaches in Advancing Modern Science and Engineering

Author

Listed:
  • Ceni Babaoglu

    (Istanbul Technical University, Faculty of Science and Letters, Department of Mathematics)

  • Irma Hacinliyan

    (Istanbul Technical University, Faculty of Science and Letters, Department of Mathematics)

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.

Suggested Citation

  • Ceni Babaoglu & Irma Hacinliyan, 2016. "Homoclinic Structure for a Generalized Davey-Stewartson System," Springer Books, in: Jacques Bélair & Ian A. Frigaard & Herb Kunze & Roman Makarov & Roderick Melnik & Raymond J. Spiteri (ed.), Mathematical and Computational Approaches in Advancing Modern Science and Engineering, pages 27-33, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-30379-6_3
    DOI: 10.1007/978-3-319-30379-6_3
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