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)
New explicit travelling wave solutions for two new integrable coupled nonlinear evolution equations. (English) Zbl 1092.35524

Summary: In this Letter, a more powerful method to seek exact travelling wave solutions of nonlinear partial differential equations is presented, which uses the good ideas of the extended-tanh function method and our previous method. The two new integrable coupled potential KdV equation and modified KdV-type equations which were firstly presented by M. V. Foursov [J. Math. Phys. 41, No. 9, 6173–6185 (2000; Zbl 0987.37064)] are chosen to illustrate the method by using symbolic computation such that multiple travelling wave solutions are obtained which contain new kink-like soliton solutions, kink-shaped solitons, bell-shaped solitons, rational solutions and singular solitons that may be useful to explain the “blow-up” phenomena.

Summary of the erratum: On page 101, there is a misprint in equation (9), which should be changed to

u(ξ)= i=1 m w i-1 A i w+B i sgn(b)(b+w 2 )+A 0 + j=0 n D j ξ j ·

On page 104, there are two misprints in equation (21), which should be changed to

u=A 0 +A 1 w+B 1 sgn(b)(b+w 2 ),v=a 0 +a 1 w+b 1 sgn(b)(b+w 2 )·

In the paragraph under equation (21), 1+sgn(b)w 2 should be changed to sgn(b)(b+w 2 ).

MSC:
35Q53KdV-like (Korteweg-de Vries) equations
35B40Asymptotic behavior of solutions of PDE
35Q51Soliton-like equations
37K10Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies