# 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 periodic solitary-wave solutions for the Benjiamin Ono equation. (English) Zbl 1185.35213
Summary: The new periodic solitary wave and doubly periodic solutions for (1 + 1)-dimensional Benjiamin Ono equation are obtained, using the bilinear method and extended homoclinic test approach. These results demonstrate that the integrable system has richly dynamical behavior even if it is (1 + 1)-dimensional.

##### MSC:
 35Q51 Soliton-like equations 35B10 Periodic solutions of PDE 35C08 Soliton solutions of PDE 37K10 Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies
Full Text:
##### References:
 [1] Korpel, A.; Banerjee, P.: Heuristic guide to nonlinear dispersive wave equation and soliton-type solution, Proc. IEEE 72, 1109-1130 (1984) [2] Fan, E.: The integrable systems and the computer algebra, (2004) [3] Fu, Z.; Liu, S.: The JEFE method and periodic solutions of two kinds of nonlinear wave equations, Commun. nonlinear sci. Numer. simulat. 8, 67-70 (2003) · Zbl 1018.35066 · doi:10.1016/S1007-5704(02)00082-5 [4] Wang, Z.; Li, D.: A method for constructing exact solutions and application to benjiamin ono equation, Chin. phys. 14, 2158-2163 (2005) [5] Dai, Z.; Huang, J.: Homoclinic orbits and periodic solitons for Boussinesq equation with even constraint, Chaos, solitons fractals 26, No. 4, 1189-1194 (2005) · Zbl 1070.35029 · doi:10.1016/j.chaos.2005.02.025 [6] Dai, Z.; Jiang, M.: Homoclinic bifurcation for Boussinesq equation with even constraint, Chin. phys. Lett. 23, 1065-1067 (2006) [7] Dai, Z.; Liu, J.; Li, D.: Applications of HTA and EHTA to YTSF equation, Appl. math. Comput. 207, 360-364 (2009) · Zbl 1159.35408 · doi:10.1016/j.amc.2008.10.042 [8] Dai, Z.; Li, Z.: 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 [9] Dai, Z.; Liu, Z.; Li, D.: Exact periodic solitary-wave solution for KdV equation, Chin. phys. Lett. 25, No. 5, 1531-1533 (2008)