Abstract
The genus-1 Kadomtsev-Petviashvili (KP)-Whitham system is derived for both variants of the KP equation; namely the KPI and KPII equations. The basic properties of the KP-Whitham system, including symmetries, exact reductions and its possible complete integrability, together with the appropriate generalization of the one-dimensional Riemann problem for the Korteweg-de Vries equation are discussed. Finally, the KP-Whitham system is used to study the linear stability properties of the genus-1 solutions of the KPI and KPII equations; it is shown that all genus-1 solutions of KPI are linearly unstable, while all genus-1 solutions of KPII are linearly stable within the context of Whitham theory.
| Original language | English |
|---|---|
| Article number | 20160695 |
| Journal | Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences |
| Volume | 473 |
| Issue number | 2204 |
| DOIs | |
| State | Published - Aug 1 2017 |
Keywords
- Dispersive regularizations
- Dispersive shock waves
- Kadomtsev-Petviashvili equation
- Small dispersion limit
- Water waves
- Whitham equations
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