On a coupled system of KP-type
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866913726877138944 |
|---|---|
| author | Aguilar, Jacob B. |
| author_facet | Aguilar, Jacob B. |
| contents | A defining characteristic of the Kadomstev-Petviashvili (KP) model equation is that the well-posedness results are subject to the restriction that at all transverse positions, the mass $\int u \,dx = \text{constant independent of $y$}.$ In 2007, for a rather general class of equations of KP type, it was shown that the zero-mass (in $x$) constraint is satisfied at any non-zero time even if it is not satisfied at initial time zero. To remedy this ``odd'' behavior, a model modification is introduced which does not impose non-physical restrictions upon the initial data. In this article, we introduce a new modified KP system, named the Non-KP model equation. After providing a variational derivation of the Non-KP model, we analyze its Hamiltonian evolutionary structure. Furthermore, we prove linear estimates in the Bourgain spaces $X^{s,b}$ corresponding to the integral equation arising from the Duhamel formulation of system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_08135 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On a coupled system of KP-type Aguilar, Jacob B. Analysis of PDEs Mathematical Physics A defining characteristic of the Kadomstev-Petviashvili (KP) model equation is that the well-posedness results are subject to the restriction that at all transverse positions, the mass $\int u \,dx = \text{constant independent of $y$}.$ In 2007, for a rather general class of equations of KP type, it was shown that the zero-mass (in $x$) constraint is satisfied at any non-zero time even if it is not satisfied at initial time zero. To remedy this ``odd'' behavior, a model modification is introduced which does not impose non-physical restrictions upon the initial data. In this article, we introduce a new modified KP system, named the Non-KP model equation. After providing a variational derivation of the Non-KP model, we analyze its Hamiltonian evolutionary structure. Furthermore, we prove linear estimates in the Bourgain spaces $X^{s,b}$ corresponding to the integral equation arising from the Duhamel formulation of system. |
| title | On a coupled system of KP-type |
| topic | Analysis of PDEs Mathematical Physics |
| url | https://arxiv.org/abs/2502.08135 |