Boosted Ground States for a Pseudo-Relativistic Schrödinger Equation with a double power nonlinearity
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866918408389394432 |
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| author | d'Avenia, Pietro Pomponio, Alessio Siciliano, Gaetano Yang, Lianfeng |
| author_facet | d'Avenia, Pietro Pomponio, Alessio Siciliano, Gaetano Yang, Lianfeng |
| contents | In this paper, we investigate the existence and limit behaviours of travelling solitary waves of the form $ψ(t,x)=e^{iλt}φ\left(x-vt\right)$ to the nonlinear pseudo-relativistic Schrödinger equation \[ i\partial_t ψ=(\sqrt{-Δ+m^2})ψ- |ψ|^{\frac{2}{N}}ψ-μ|ψ|^{q}ψ~~\text{ on }\mathbb{R}^N, \] for $m\ge 0$ and $|v|<1$. To this end, we introduce and analyse an associated constrained variational problem, whose minimizers are termed boosted ground states and the parameter $λ$ is obtained as a Lagrangian multiplier. We first provide a complete classification for the existence and nonexistence of such boosted ground states. Based on this classification, we then study several limiting profiles, for which the exact blow-up rate is also established. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_24449 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Boosted Ground States for a Pseudo-Relativistic Schrödinger Equation with a double power nonlinearity d'Avenia, Pietro Pomponio, Alessio Siciliano, Gaetano Yang, Lianfeng Analysis of PDEs 35S05, 35R11, 35J60 In this paper, we investigate the existence and limit behaviours of travelling solitary waves of the form $ψ(t,x)=e^{iλt}φ\left(x-vt\right)$ to the nonlinear pseudo-relativistic Schrödinger equation \[ i\partial_t ψ=(\sqrt{-Δ+m^2})ψ- |ψ|^{\frac{2}{N}}ψ-μ|ψ|^{q}ψ~~\text{ on }\mathbb{R}^N, \] for $m\ge 0$ and $|v|<1$. To this end, we introduce and analyse an associated constrained variational problem, whose minimizers are termed boosted ground states and the parameter $λ$ is obtained as a Lagrangian multiplier. We first provide a complete classification for the existence and nonexistence of such boosted ground states. Based on this classification, we then study several limiting profiles, for which the exact blow-up rate is also established. |
| title | Boosted Ground States for a Pseudo-Relativistic Schrödinger Equation with a double power nonlinearity |
| topic | Analysis of PDEs 35S05, 35R11, 35J60 |
| url | https://arxiv.org/abs/2603.24449 |