2006/01/12 by C. Klein, P. Markowich, C. Sparber · 3 citations
Physics and Astronomy · Mathematics · #math-ph #math.MP #nlin.SI #msc:37K10 #msc:35Q53 #msc:34E05 #msc:35Q55
paper · pdf · doi:10.1007/s00332-007-9001-y
39 pages, 36 figures (high resolution figures at http://www.mis.mpg.de/preprints/index.html)
arxiv created 2006/01/12 · arxiv updated 2009/12/01
The aim of this paper is the accurate numerical study of the KP equation. In particular we are concerned with the small dispersion limit of this model, where no comprehensive analytical description exists so far. To this end we first study a similar highly oscillatory regime for asymptotically small solutions, which can be described via the Davey-Stewartson system. In a second step we investigate numerically the small dispersion limit of the KP model in the case of large amplitudes. Similarities and differences to the much better studied Korteweg-de Vries situation are discussed as well as the dependence of the limit on the additional transverse coordinate.