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)
The Cole-Hopf transformation and improved tanh-coth method applied to new integrable system (KdV6). (English) Zbl 1157.65457
Summary: We study a new coupled system (KdV6) from the point of view of constructing exact solutions for it by using the Cole-Hopf transformation and one improved tanh-coth method. Traveling wave solutions which include periodic and soliton solutions are formally derived.

MSC:
65M70Spectral, collocation and related methods (IVP of PDE)
35Q53KdV-like (Korteweg-de Vries) equations
37K10Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies
35Q51Soliton-like equations
Software:
Mathematica
WorldCat.org
Full Text: DOI
References:
[1] Dye, J. M.; Parker, A.: On bidirectional nonlinear fifth-order nonlinear evolution equations, Lax pairs, and directionally dependent solitary waves. J. math. Phys. 42, 2567-2589 (2001) · Zbl 1061.37048
[2] Karasu-Kalcanli, A.; Sakovich, S.: Bäcklund transformation and special solutions for the Drinfeld -- sokolev -- satsuma -- Hirota system of coupled equations. J. phys. A: math. Gen. 34, 7355-7358 (2001) · Zbl 0983.35116
[3] Verhoeven, C.; Musette, M.: Solution solutions of two bidirectional sixth-order partial differential equations belonging to the KP hierarchy. J. phys. A: math. Gen. 36, L133-L143 (2003) · Zbl 1039.35109
[4] A. Karasu-Kalcanli, A. Karasu, A. Sakovich, S. Sakovich, R. Turhan, A new integrable generalization of the Korteweg-de Vries equation, Available from: arXiv: nlin 0708.3247 v1, [nlin.SI], 23 August 2007. · Zbl 1152.35473
[5] B.A. Kupershmidt, KdV6: an integrable system, Available from: arXiv: nlin 0709.3848 v1, [nlin.SI], 24 September 2007.
[6] Wazwaz, A. M.: The extended tanh method for new solitons solutions for many forms of the fifth-order KdV equations. Appl. math. Comput. 84, No. 2, 1002-1014 (2007) · Zbl 1115.65106
[7] A. Salas, C.A. Gomez, A practical approach to solve coupled systems of nonlinear partial differential equations, Available from: arXiv: 0805.3670 [math-ph], 23 May 2008.