Displaying similar documents to “Stability of standing waves for nonlinear Schrödinger equations with potentials”

Stability and Instability of Solitary Wave Solutions of a Nonlinear Dispersive System of Benjamin-Bona-Mahony Type

Hakkaev, Sevdzhan (2003)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: 35B35, 35B40, 35Q35, 76B25, 76E30. This paper concerns the orbital stability and instability of solitary waves of the system of coupling equations of Benjamin-Bona-Mahony type. By applying the abstract results of Grillakis, Shatah and Strauss and detailed spectral analysis, we obtain the existence and stability of the solitary waves. Partially Supported by Grant MM-810/98 of MESC and by Scientefic Research Grant 19/12.03.2003...

On the inhomogeneous nonlinear Schrödinger equation with harmonic potential and unbounded coefficient

Jianqing Chen (2010)

Czechoslovak Mathematical Journal

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By deriving a variant of interpolation inequality, we obtain a sharp criterion for global existence and blow-up of solutions to the inhomogeneous nonlinear Schrödinger equation with harmonic potential i ϕ t = - ▵ ϕ + | x | 2 ϕ - | x | b | ϕ | p - 2 ϕ . We also prove the existence of unstable standing-wave solutions via blow-up under certain conditions on the unbounded inhomogeneity and the power of nonlinearity, as well as the frequency of the wave.