zbMATH — the first resource for mathematics

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.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
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)
Exact homoclinic wave and soliton solutions for the 2D Ginzburg-Landau equation. (English) Zbl 1220.35168
Summary: New exact wave solutions including homoclinic wave, kink wave and soliton solutions for the 2D Ginzburg-Landau equation are obtained using the auxiliary function method, generalized Hirota method and the ansatz function technique under the certain constraint conditions of coefficients in equation, respectively. The result shows that there exists a kink-wave solution which tends to one and the same periodic wave solution as time tends to infinite.

35Q56Ginzburg-Landau equations
35Q51Soliton-like equations
Full Text: DOI
[1] Temam, R.: Infinite-dimensional dynamical systems in mechanics and physics. (2001)
[2] Blennerhassett, P. J.: Philos. trans. R. soc. London, ser. A. 298, 451 (1980)
[3] Moon, H. T.; Huerre, P.; Redekopp, L. G.: Phys. rev. Lett.. 49, 485 (1982)
[4] Moon, H. T.; Huerre, P.; Redekopp, L. G.: Physica D. 7, 135 (1983)
[5] Fang, F.; Xiao, Y.: Opt. commun.. 268, No. 2, 305 (2006)
[6] Abdul-Majida; Wazwaz: Appl. math. Lett.. 19, No. 10, 1007 (2006)
[7] Ablowitz, M. J.; Clarkson, P. A.: Solitons, nonlinear evolution and inverse scattering. (1991) · Zbl 0762.35001
[8] Dai, Z.; Li, S.; Li, D.; Zhu, A.: Chaos solitons fractals. 34, No. 4, 1148 (2007)
[9] Van Saarloos, W.; Hohenberg, P. C.: Physica D. 56, 303 (1992)
[10] Akhmediev, N.; Ankiewicz, A.: Solitons. nonlinear pulses and beams. (1997)
[11] Zhou, Y. B.; Wang, M. L.: Phys. lett. A. 308, 31 (2003)
[12] Zhou, Y.; Wang, M.; Miao, T.: Phys. lett. A. 323, 77 (2004)