Towards a rigorous derivation of the fifth order KP equation

Lionel Paumond

Mathematics and Computers in Simulation (MATCOM), 2005, vol. 69, issue 5, 477-491

Abstract: The Kadomtsev–Petviashvili equations (KP) are universal models for dispersive, weakly nonlinear, almost one-dimensional long waves of small amplitude. In [L. Paumond, A rigorous link between KP and a Benney–Luke equation, Differential Integral Equations 16 (9) (2003) 1039–1064], we proved a rigorous link between KP and a Benney–Luke equation. Here, we derive a new model still valid when the Bond number is equal to 1/3. Following the work [R.L. Pego, J.R. Quintero, Two-dimensional solitary waves for a Benney–Luke equation, Physica D 132 (4) (1999) 476–496], we show the existence of solitary waves for this equation and their convergence towards the solitary waves of the fifth order KP equation. We also link rigorously the dynamics of the two equations.

Date: 2005
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378475405000960
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:69:y:2005:i:5:p:477-491

DOI: 10.1016/j.matcom.2005.03.012

Access Statistics for this article

Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens

More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier
Bibliographic data for series maintained by Catherine Liu ().