紀要論文

紀要論文

text

Osaka Journal of Mathematics. 2019, 56(4), p. 713-726

STRONG INSTABILITY OF STANDING WAVES FOR NONLINEAR SCHRÖDINGER EQUATIONS WITH ATTRACTIVE INVERSE POWER POTENTIAL

Osaka University and Osaka City University, Departments of Mathematics

英語

text

2019-10

We study the strong instability of standing waves e＾<iωt>φ_ω(x) for nonlinear Schrödinger equations with an L²-supercritical nonlinearity and an attractive inverse power potential, where ω ∈ ℝ is a frequency, and φ_ω ∈ H¹(ℝ＾N) is a ground state of the corresponding stationary equation. Recently, for nonlinear Schrödinger equations with a harmonic potential, Ohta (2018) proved that if ∂²_λS_ω(φ＾λ_ω)|_<λ=1> ≤ 0, then the standing wave is strongly unstable, where S_ω is the action, and φ^λ_ω (x) := λ^<N/2> φ_ω (λx) is the scaling, which does not change the L²-norm. In this paper, we prove the strong instability under the same assumption as the above-mentioned in inverse power potential case. Our proof is applicable to nonlinear Schrödinger equations with other potentials such as an attractive Dirac delta potential.

10.18910/73624

73624

STRONG INSTABILITY OF STANDING WAVES FOR NONLINEAR SCHRÖDINGER EQUATIONS WITH ATTRACTIVE INVERSE POWER POTENTIAL

Osaka University and Osaka City University, Departments of Mathematics

英語

2019-10

Osaka Journal of Mathematics

56

4

713

726

https://hdl.handle.net/11094/73624

10.18910/73624

https://doi.org/10.18910/73624