Instability of standing waves for nonlinear Schrdinger equations with inhomogeneous nonlinearities

@inproceedings{Fukuizumi2004InstabilityOS,
  title={Instability of standing waves for nonlinear Schrdinger equations with inhomogeneous nonlinearities},
  author={Reika Fukuizumi and Masahito Ohta},
  year={2004}
}
The effect of inhomogeneity of nonlinear medium is discussed concerning the stability of standing waves eφω(x) for a nonlinear Schrödinger equation with an inhomogeneous nonlinearity V (x)|u|p−1u, where V (x) is proportional to the electron density. Here, ω > 0 and φω(x) is a ground state of the stationary problem. When V (x) behaves like |x|−b at infinity, where 0 < b < 2, we show that eφω(x) is stable for p < 1 + (4− 2b)/n and sufficiently small ω > 0. The main point of this paper is to… CONTINUE READING

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