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Zbl 1064.35176
Babaoglu, Ceni; Eden, Alp; Erbay, Saadet
Global existence and nonexistence results for a generalized Davey-Stewartson system. (English)
[J] J. Phys. A, Math. Gen. 37, No. 48, 11531-11546 (2004). ISSN 0305-4470

Summary: The authors consider a system of three equations, which will be called generalized Davey-Stewartson equations, involving three coupled equations, two for the long waves and one for the short wave propagating in an infinite elastic medium. They classify the system according to the signs of the parameters. Conserved quantities related to mass, momentum and energy are derived as well as a specific instance of the so-called virial theorem. Using these conservation laws and the virial theorem both global existence and nonexistence results are established under different constraints on the parameters in the elliptic-elliptic-elliptic case.

MSC 2000:: *35Q55 NLS-like (nonlinear Schroedinger) equations
76B15 Wave motions (fluid mechanics)

Keywords: long waves; short wave; infinite elastic medium; Conserved quantities; existence; nonexistence

Cited in: Zbl 1152.35492

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