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Nonlinear, nondispersive wave equations: Lagrangian and Hamiltonian functions in the hodograph transformation
https://repo.qst.go.jp/records/79751
https://repo.qst.go.jp/records/79751c4f3e57c-c937-491a-8469-25c815bccd09
| Item type | 学術雑誌論文 / Journal Article(1) | |||||
|---|---|---|---|---|---|---|
| 公開日 | 2020-04-01 | |||||
| タイトル | ||||||
| タイトル | Nonlinear, nondispersive wave equations: Lagrangian and Hamiltonian functions in the hodograph transformation | |||||
| 言語 | ||||||
| 言語 | eng | |||||
| 資源タイプ | ||||||
| 資源タイプ識別子 | http://purl.org/coar/resource_type/c_6501 | |||||
| 資源タイプ | journal article | |||||
| アクセス権 | ||||||
| アクセス権 | metadata only access | |||||
| アクセス権URI | http://purl.org/coar/access_right/c_14cb | |||||
| 著者 |
Pegoraro, Francesco
× Pegoraro, Francesco× Bulanov, Sergey× Bulanov, Sergey |
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| 抄録 | ||||||
| 内容記述タイプ | Abstract | |||||
| 内容記述 | The hodograph transformation is generally used in order to associate a system of linear partial differential equations to a system of nonlinear (quasilinear) differential equations by interchanging dependent and independent variables. Here we consider the case when the nonlinear differential system can be derived from a Lagrangian density and revisit the hodograph transformation within the formalism of the Lagrangian-Hamiltonian continuous dynamical systems. Restricting to the case of nondissipative, nondispersive one-dimensional waves, we show that the hodograph transformation leads to a linear partial differential equation for an unknown function that plays the role of the Lagrangian in the hodograph variables. We then define the corresponding hodograph Hamiltonian and show that it turns out to coincide with the wave amplitude. i.e., with the unknown function of the independent variables to be solved for in the initial nonlinear wave equation. |
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| 書誌情報 |
Physics Letters A 巻 384, 号 2, 発行日 2020-01 |
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| ISSN | ||||||
| 収録物識別子タイプ | ISSN | |||||
| 収録物識別子 | 0375-9601 | |||||
| DOI | ||||||
| 識別子タイプ | DOI | |||||
| 関連識別子 | 10.1016/j.physleta.2019.126064 | |||||
| 関連サイト | ||||||
| 識別子タイプ | URI | |||||
| 関連識別子 | https://www.sciencedirect.com/science/article/abs/pii/S0375960119309545#! | |||||
