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)
On the periodic solutions for both nonlinear differential and difference equations: a unified approach. (English) Zbl 1238.35060
Summary: A direct and unifying scheme for disclosure of periodic wave solutions of both nonlinear differential and difference equations is presented. The scheme is based on Hirota’s bilinear form and certain Riemann theta function formulae. The relations between periodic wave solutions and soliton solutions are rigorously established.

MSC:
35L70Nonlinear second-order hyperbolic equations
39A14Partial difference equations
39A23Periodic solutions (difference equations)
35C07Traveling wave solutions of PDE
35C08Soliton solutions of PDE
14K25Theta-functions
WorldCat.org
Full Text: DOI
References:
[1] Hirota, R.; Satsuma, J.: Prog. theor. Phys., Prog. theor. Phys. 57, 797 (1977)
[2] Hirota, R.: Direct methods in soliton theory, (2004) · Zbl 1099.35111
[3] Hu, X. B.; Li, C. X.; Nimmo, J. J. C.; Yu, G. F.: J. phys. A, J. phys. A 38, 195 (2005)
[4] Hirota, R.; Ohta, Y.: J. phys. Soc. jpn., J. phys. Soc. jpn. 60, 798 (1991)
[5] Sawada, K.; Kotera, T.: Prog. theor. Phys., Prog. theor. Phys. 51, 1355 (1974)
[6] Chow, K. W.: J. math. Phys., J. math. Phys. 35, 4057 (1994)
[7] Chow, K. W.: J. math. Phys., J. math. Phys. 36, 4125 (1995)
[8] Chow, K. W.: Wave motion, Wave motion 35, 71 (2002)
[9] Chow, K. W.; Mark, C. C.; Rogers, C.; Schief, W. K.: J. comput. Appl. mech., J. comput. Appl. mech. 190, 114 (2006)
[10] Nakamura, A.: J. phys. Soc. jpn., J. phys. Soc. jpn. 47, 1701 (1979)
[11] Nakamura, A.: J. phys. Soc. jpn., J. phys. Soc. jpn. 48, 1365 (1980)
[12] Dai, H. H.; Fan, E. G.; Geng, X. G.:
[13] Zhang, Y.; Ye, L. Y.; Lv, Y. N.; Zhao, H. Q.: J. phys. A, J. phys. A 40, 5539 (2007)
[14] Hon, Y. C.; Fan, E. G.; Qin, Z. Y.: Mod. phys. Lett. B, Mod. phys. Lett. B 22, 547 (2008)
[15] Fan, E. G.; Hon, Y. C.: Phys. rev. E, Phys. rev. E 78, 036607 (2008)
[16] Fan, E. G.: J. phys. A, J. phys. A 42, 095206 (2009)
[17] Ma, W. X.; Zhou, R. G.; Gao, L.: Mod. phys. Lett. A, Mod. phys. Lett. A 24, 1677 (2009)
[18] Farkas, H. M.; Kra, I.: Riemann surfaces, (1992) · Zbl 0764.30001
[19] Mumford, D.: Theta lectures on theta II, (1983) · Zbl 0509.14049
[20] Yu, S. J.; Toda, K.; Sasa, N.; Fukuyama, T.: J. phys. A, J. phys. A 31, 3337 (1998) · Zbl 0927.35102
[21] Bogoyavenskii, O. I.: Math. USSR izv., Math. USSR izv. 36, 129 (1991)
[22] Hirota, R.; Satsuma, J.: Progr. theor. Phys. suppl., Progr. theor. Phys. suppl. 64, 64 (1976)
[23] Hu, X. B.; Clarkson, P. A.: J. phys. A, J. phys. A 28, 5009 (1995)
[24] Ma, W. X.: Chaos solitons fractals, Chaos solitons fractals 19, 163 (2004)
[25] Ma, W. X.; Li, C. X.; He, J.: Nonlinear anal., Nonlinear anal. 70, 4245 (2009)