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Instability of ground states for a quasilinear Schrödinger equation. (English) Zbl 1340.35320
Summary: We study a class of one parameter (denoted by \(\kappa\)) family of quasi-linear Schrödinger equations arising in the theory of superfluid film in plasma physics. Using variational techniques, we prove the orbital instability of solitary waves for small values of the parameter \(\kappa\), which gives an answer to a question raised in [M. Colin et al., Nonlinearity 23, No. 6, 1353–1385 (2010; Zbl 1192.35163)].

MSC:
35Q55 NLS equations (nonlinear Schrödinger equations)
35B35 Stability in context of PDEs
35A15 Variational methods applied to PDEs
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