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)
Applications of HTA and EHTA to YTSF equation. (English) Zbl 1159.35408
Summary: Homoclinic test approach (HTA) and extended homoclinic test approach (EHTA) are proposed to seek solitary-wave solution of high dimensional nonlinear wave system. Exact periodic solitary-wave, periodic soliton, cross solitary-wave and doubly periodic wave solutions for YTSF equation are obtained using HTA and EHTA, respectively.
MSC:
35Q53KdV-like (Korteweg-de Vries) equations
35Q51Soliton-like equations
35B10Periodic solutions of PDE
References:
[1]M. Tajiri, T. Arai, Periodic soliton solutions to the Davey – Stewartson equation, in: Proceedings of the Institute of Math. of NAS of Ukraine, vol. 30, 2000, pp. 210 – 217. · Zbl 0956.35117
[2]Yomba, E.: Construction of new soliton-like solutions for the (2+1)dimensional Kadomtsev – Petviashvili equation, Chaos solitons fract 22, 321-325 (2004) · Zbl 1063.35141 · doi:10.1016/j.chaos.2004.02.001
[3]Ablowitz, M. J.; Clarkson, P. A.: Solitons, nonlinear evolution equations and inverse scattering, (1991) · Zbl 0762.35001
[4]Konopechenko, B.: Solitons in multidimensions, inverse spectral transform method, (1993) · Zbl 0836.35002
[5]Dai, Z.; Li, S.; Li, D.; Zhu, A.: Periodic bifurcation and soliton deflexion for Kadomtsev – Petviashvili equation, Chin. phys. Lett. 24, 1429-1433 (2007)
[6]Yu, S. J.; Toda, K.; Sasa, N.; Fukuyama, T.: N soliton solutions to the bogoyavlenskii – schiff equation and a quest for the soliton solution in (3+1) dimensions, J. phys. A: math. Gen. 31, 3337-3347 (1998) · Zbl 0927.35102 · doi:10.1088/0305-4470/31/14/018
[7]Schff, J.: Painlevé transendent, Their asymptotics and physical applications (1992)
[8]Yan, Z.: New families of nontravelling wave solutions to a new (3+1)-dimensional potential-YTSF equation, Phys. lett. A 318, 78-83 (2003) · Zbl 1045.35072 · doi:10.1016/j.physleta.2003.08.073
[9]Dai, Z.; Huang, J.; Jiang, M.: Explicit homoclinic tube solutions and chaos for Zakharov system with periodic boundary, Phys. lett. A 352, 411-415 (2006) · Zbl 1187.37112 · doi:10.1016/j.physleta.2005.12.026
[10]Dai, Z.; Huang, J.: Homoclinic tubes for the Davey – Stewartson II equation with periodic boundary conditions, J. chin. Phys. 43, 349-360 (2005)
[11]Dai, Z.; Li, Z.; Liu, Z.; Li, D.: Exact homoclinic wave and soliton solutions for the 2D Ginzburg – Landau equation, Phys. lett. A 372, 3010-3014 (2008) · Zbl 1220.35168 · doi:10.1016/j.physleta.2008.01.015
[12]Dai, Z.; Jiang, M.; Dai, Q.; Li, S.: Homoclinic bifurcation for Boussinesq equation with even constraint, Chin. phys. Lett. 23, 1065-1067 (2006)
[13]Dai, Z.; Huang, J.; Jiang, M.; Wang, S.: Homoclinic orbits and periodic solitons for Boussinesq equation with even constraint, Chaos solitons fract. 26, 1189-1194 (2005) · Zbl 1070.35029 · doi:10.1016/j.chaos.2005.02.025
[14]Dai, Z.; Li, S.; Dai, Q.; Huang, J.: Singular periodic soliton solutions and resonance for the Kadomtsev – Petviashvili equation, Chaos solitons fract. 34, 1148-1153 (2007) · Zbl 1142.35563 · doi:10.1016/j.chaos.2006.04.028
[15]Dai, Z.; Liu, Z.; Li, D.: Exact periodic solitary-wave solution for KdV equation, Chin. phys. Lett. 25, 1531-1533 (2008)