Instability of the standing waves for the nonlinear Klein-Gordon equations in one dimension

@inproceedings{Wu2017InstabilityOT,
  title={Instability of the standing waves for the nonlinear Klein-Gordon equations in one dimension},
  author={Yifei Wu},
  year={2017}
}
In this paper, we consider the following nonlinear Klein-Gordon equation ∂ttu−∆u+ u = |u|u, t ∈ R, x ∈ R, with 1 < p < 1 + 4 d . The equation has the standing wave solutions uω = e φω with the frequency ω ∈ (−1, 1), where φω obeys −∆φ+ (1− ω)φ− φ = 0. It was proved by Shatah (1983), and Shatah, Strauss (1985) that there exists a critical frequency ωc ∈ (0, 1) such that the standing waves solution uω is orbitally stable when ωc < |ω| < 1, and orbitally unstable when |ω| < ωc. Further, the… CONTINUE READING

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