The aim of this paper is to survey and complete, mostly by numerical simulations, results on a remarkable Boussinesq system describing weakly nonlinear, long surface water waves. It is the only member of the so-called (abcd) family of Boussinesq systems known to be completely integrable.
1
Université de Bourgogne, Dijon, France; Institut Universitaire de France, Paris, France
2
Université Paris-Saclay et CNRS, Orsay, France
Christian Klein; Jean-Claude Saut. On the Kaup–Broer–Kupershmidt systems. EMS surveys in mathematical sciences, Tome 12 (2025) no. 1, pp. 215-242. doi: 10.4171/emss/98
@article{10_4171_emss_98,
author = {Christian Klein and Jean-Claude Saut},
title = {On the {Kaup{\textendash}Broer{\textendash}Kupershmidt} systems},
journal = {EMS surveys in mathematical sciences},
pages = {215--242},
year = {2025},
volume = {12},
number = {1},
doi = {10.4171/emss/98},
url = {http://geodesic.mathdoc.fr/articles/10.4171/emss/98/}
}
TY - JOUR
AU - Christian Klein
AU - Jean-Claude Saut
TI - On the Kaup–Broer–Kupershmidt systems
JO - EMS surveys in mathematical sciences
PY - 2025
SP - 215
EP - 242
VL - 12
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.4171/emss/98/
DO - 10.4171/emss/98
ID - 10_4171_emss_98
ER -
%0 Journal Article
%A Christian Klein
%A Jean-Claude Saut
%T On the Kaup–Broer–Kupershmidt systems
%J EMS surveys in mathematical sciences
%D 2025
%P 215-242
%V 12
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4171/emss/98/
%R 10.4171/emss/98
%F 10_4171_emss_98
