تقرير
Hamiltonian aspects of the kinetic equation for soliton gas
| العنوان: | Hamiltonian aspects of the kinetic equation for soliton gas |
|---|---|
| المؤلفون: | Vergallo, Pierandrea, Ferapontov, Evgeny V. |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics Mathematical Physics Nonlinear Sciences |
| مصطلحات موضوعية: | Nonlinear Sciences - Exactly Solvable and Integrable Systems, Mathematical Physics, Nonlinear Sciences - Pattern Formation and Solitons |
| الوصف: | We investigate Hamiltonian aspects of the integro-differential kinetic equation for dense soliton gas which results as a thermodynamic limit of the Whitham equations. Under a delta-functional ansatz, the kinetic equation reduces to a non-diagonalisable system of hydrodynamic type whose matrix consists of several $2\times 2$ Jordan blocks. We demonstrate that the resulting system possesses local Hamiltonian structures of differential-geometric type, for all standard two-soliton interaction kernels (KdV, sinh-Gordon, hard-rod, Lieb-Liniger, DNLS, and separable cases). In the hard-rod case, we show that the continuum limit of these structures provides a local multi-Hamiltonian formulation of the full kinetic equation. |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2403.20162 |
| رقم الأكسشن: | edsarx.2403.20162 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |