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 analytic solutions of stochastic coupled KdV equations. (English) Zbl 1198.35292
Summary: Firstly, we use the exp-function method to seek new exact solutions of the Riccati equation. Then, with the help of Hermit transformation, we employ the Riccati equation and its new exact solutions to find new analytic solutions of the stochastic coupled KdV equation in the white noise environment. As some special examples, some analytic solutions can degenerate into these solutions reported in open literatures. Editorial remark: There are doubts about a proper peer-reviewing procedure of this journal. The editor-in-chief has retired, but, according to a statement of the publisher, articles accepted under his guidance are published without additional control.

MSC:
35R60PDEs with randomness, stochastic PDE
35Q53KdV-like (Korteweg-de Vries) equations
WorldCat.org
Full Text: DOI
References:
[1] Wadati, M.: Stochastic Korteweg -- de Vries equation, J phys soc jpn 52, 2642 (1983)
[2] Wadati, M.; Akutsu, Y.: Stochastic Korteweg -- de Vries equation with and without damping, J phys soc jpn 53, 3342 (1984)
[3] Wadati, M.: Deformation of solitons in random media, J phys soc jpn 59, 4201 (1990) · Zbl 0737.35088 · doi:10.1143/JPSJ.59.4201
[4] Holden, H.; øendal, B.; Ubøe, J.; Zhang, T.: Stochastic partial differential equations, (1996) · Zbl 0860.60045
[5] Xie, Y. C.: Exact solutions for Wick-type stochastic coupled KdV equations, Phys lett A 327, 174 (2004) · Zbl 1138.35419 · doi:10.1016/j.physleta.2004.05.026
[6] Chen, Y.; Wang, Q.; Li, B.: The stochastic soliton-like solutions of stochastic KdV equations, Chaos, solitons and fractals 23, 1465 (2005) · Zbl 1086.35088 · doi:10.1016/j.chaos.2004.06.049
[7] Liu, Q.: Uniformly constructing a series of exact solutions for (2+1)-dimensional stochastic Broer -- Kaup system, Chaos, solitons and fractals 36, 1037 (2008) · Zbl 1132.35457 · doi:10.1016/j.chaos.2006.08.002
[8] He, J. H.; Wu, X. H.: Exp-function method for nonlinear wave equations, Chaos, solitons and fractals 30, 700 (2006) · Zbl 1141.35448 · doi:10.1016/j.chaos.2006.03.020
[9] Ma, Z. Y.; Zhu, J. M.: Jacobian elliptic function expansion solutions for the Wick-type stochastic coupled KdV equations, Chaos, solitons and fractals 32, 1679 (2007) · Zbl 1225.35202 · doi:10.1016/j.chaos.2005.11.085
[10] Dai, C. Q.; Wang, Y. Y.: New exact solutions of the (3+1)-dimensional Burgers system, Phys lett A 373, 181 (2009) · Zbl 1227.35231
[11] Yan, Z. Y.; Zhang, H. Q.: New explicit solitary wave solutions and periodic wave solutions for Whitham -- Broer -- Kaup equation in shallow water, Phys lett A 285, 355 (2001) · Zbl 0969.76518
[12] Rössler, O. E.: An equation for continuous chaos, Phys lett A 57, 397 (1976)