Spectral instability of peakons for the b-family of Novikov equations
arxiv(2024)
摘要
In this paper, we are concerned with a one-parameter family of peakon
equations with cubic nonlinearity parametrized by a parameter usually denoted
by the letter b. This family is called the “b-Novikov” since it reduces
to the integrable Novikov equation in the case b=3. By extending the
corresponding linearized operator defined on functions in H^1(ℝ) to
one defined on weaker functions on L^2(ℝ), we prove spectral and
linear instability on of peakons in the b-Novikov equations for any
b. We also consider the stability on and show that the peakons are
spectrally or linearly stable only in the case b=3.
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