Homoclinic Structure for a Generalized Davey-Stewartson System

Ceni Babaoglu () and Irma Hacinliyan ()
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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

A chapter in Mathematical and Computational Approaches in Advancing Modern Science and Engineering, 2016, pp 27-33 from Springer

Abstract: 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.

Keywords: Couple Stress; Homoclinic Orbit; Linearize Stability Analysis; Group Speed; Order Linear System (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-30379-6_3

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

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