On travelling wave solutions of a generalized Davey-Stewartson system

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Tarih

2005-02

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Yayıncı

Oxford Univ Press

Erişim Hakkı

info:eu-repo/semantics/closedAccess

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Özet

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, m(1), m(2), 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.

Açıklama

Anahtar Kelimeler

Packets, Equation, Soliton, Davey-Stewartson equations, Nonlinear Schrodinger equation, Pohozaev identity, Radial solutions, Travelling wave, Integral equations, Mathematical models, Nonlinear equations, Wave propagation, Elasticity

Kaynak

IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)

WoS Q Değeri

Q3
Q3

Scopus Q Değeri

Q3

Cilt

70

Sayı

1

Künye

Eden, A. & Erbay, S. (2005; 2004). On travelling wave solutions of a generalized davey-stewartson system. IMA Journal of Applied Mathematics (Institute of Mathematics and its Applications), 70(1), 15-24. doi:10.1093/imamat/hxh050