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)
Multisoliton solutions of the Degasperis-Procesi equation and their peakon limit. (English) Zbl 1086.35095

Summary: The multisoliton solutions of the Degasperis-Procesi (DP) equation are constructed by means of a reduction procedure (CKP reduction) for the multisoliton solutions of the Kadomtsev-Petviashvili hierarchy. The solutions have parametric representations and exhibit several new features when compared with existing soliton solutions. Of particular interest are the one- and two-soliton solutions for which a detailed analysis is performed. The explicit formula for the phase shift is obtained which occurs in the interaction process of two solitons. We find that the soliton velocity depends nonlinearly on its amplitude as opposed to the usual linear relation. Also, the interaction of two solitons reveals that the slow soliton exhibits a nonnegative phase shift in a certain range of the wave parameters.

Subsequently, we consider the peakon limit of the soliton solutions and show that it recovers all the features already reported for the peakon solutions of the DP equation. We also derive the asymptotic form of the general N-soliton solution as well as the formula for the phase shift.


MSC:
35Q53KdV-like (Korteweg-de Vries) equations
37K40Soliton theory, asymptotic behavior of solutions
37K10Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies
35Q51Soliton-like equations