zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Camassa-Holm, Korteweg-de Vries and related models for water waves. (English) Zbl 1037.76006
This paper studies Korteweg-de Vries (KdV) equation, shallow-water equation, regularized long-wave equation, Camassa-Holm (CH) equation, and Green-Naghdi equation. The author describes the current methods for obtaining the CH equation in the context of water wave theory, presents the corresponding higher-order KdV results that are, in a sense, an analogue of the CH equation,and show that the CH equation does indeed arise in the water-wave problem, but in a careful limiting process. Moreover, some properties of this equation, and how it relates to the description of surface waves, are discussed. Finally, a possibility of extending the calculations to different scenarios is addressed, and, as an example, a two-dimensional CH equation is derived for water waves.
MSC:
76B15Water waves, gravity waves; dispersion and scattering, nonlinear interaction
35Q35PDEs in connection with fluid mechanics
35Q53KdV-like (Korteweg-de Vries) equations