2024/02/13 by Deng, Xijun, Lafortune, Stéphane
#35B35 #35C08 #35P05 #35Q35 #Analysis of PDEs (math.AP) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences
paper · doi:10.48550/arxiv.2402.08759
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 H1(ℝ) to one defined on weaker functions on L2(ℝ), we prove spectral and linear instability on L2(ℝ) of peakons in the b-Novikov equations for any b. We also consider the stability on H1(ℝ) and show that the peakons are spectrally or linearly stable only in the case b=3.