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Global existence and nonexistence results for a generalized Davey-Stewartson system. (English) Zbl 1064.35176
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:
35Q55NLS-like (nonlinear Schrödinger) equations
76B15Water waves, gravity waves; dispersion and scattering, nonlinear interaction