Spectral instability of peakons for the $b$-family of Novikov equations
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866916404752547840 |
|---|---|
| author | Deng, Xijun Lafortune, Stéphane |
| author_facet | Deng, Xijun Lafortune, Stéphane |
| contents | 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 $H^1(\mathbb{R})$ to one defined on weaker functions on $L^2(\mathbb{R})$, we prove spectral and linear instability on $L^2(\mathbb{R})$ of peakons in the $b$-Novikov equations for any $b$. We also consider the stability on $H^1(\mathbb{R})$ and show that the peakons are spectrally or linearly stable only in the case $b=3$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_08759 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Spectral instability of peakons for the $b$-family of Novikov equations Deng, Xijun Lafortune, Stéphane Analysis of PDEs Exactly Solvable and Integrable Systems 35B35, 35C08, 35P05, 35Q35 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 $H^1(\mathbb{R})$ to one defined on weaker functions on $L^2(\mathbb{R})$, we prove spectral and linear instability on $L^2(\mathbb{R})$ of peakons in the $b$-Novikov equations for any $b$. We also consider the stability on $H^1(\mathbb{R})$ and show that the peakons are spectrally or linearly stable only in the case $b=3$. |
| title | Spectral instability of peakons for the $b$-family of Novikov equations |
| topic | Analysis of PDEs Exactly Solvable and Integrable Systems 35B35, 35C08, 35P05, 35Q35 |
| url | https://arxiv.org/abs/2402.08759 |