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)
Jacobi elliptic function solutions of the Ablowitz-Ladik discrete nonlinear Schrödinger system. (English) Zbl 1197.81121
Summary: A new general Jacobi elliptic function expansion algorithm is developed to obtain exact solutions for discrete nonlinear systems. Applying this method, many exact Jabobi elliptic function travelling wave solutions for Ablowitz-Ladik discrete nonlinear Schrödinger system are derived. These doubly periodic solutions may degenerate to hyperbolic function solutions including discrete soliton solutions as the modulus $m \rightarrow 1$ and trigonometric function solutions as $m \rightarrow 0$, respectively. 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:
81Q05Closed and approximate solutions to quantum-mechanical equations
35J99Elliptic equations and systems
35Q55NLS-like (nonlinear Schrödinger) equations
WorldCat.org
Full Text: DOI
References:
[1] Fermi, E.; Pasta, J.; Ulam, S.: Collected papers of enrico Fermi, (1965)
[2] Levi, D.; Ragnisco, O.: Lett nuovo cimento, Lett nuovo cimento 22, 691 (1978)
[3] Sokolov, V. V.; Shabat, A. B.: Sov sci rev C: Math phys rev, Sov sci rev C: Math phys rev 4, 221 (1984)
[4] Svinolupov, S. I.; Yamilov, R. I.: Phys lett A, Phys lett A 160, 548 (1991)
[5] Adler, V. E.; Svinolupov, S. I.; Yamilov, R. I.: Phys lett A, Phys lett A 254, 24 (1999)
[6] Cherdantsev, Iyu; Yamilov, R. I.: Phys D, Phys D 87, 140 (1995)
[7] Shabat, A. B.; Yamilov, R. I.: Leningrad math J, Leningrad math J 2, 377 (1991)
[8] Yang, H. X.; Xu, X. X.; Ding, H. Y.: Chaos, solitons & fractals, Chaos, solitons & fractals 26, 1091 (2005)
[9] Zhang, D. J.: Chaos, solitons & fractals, Chaos, solitons & fractals 23, 1333 (2005)
[10] Gordoa, P. R.; Pickering, A.; Zhu, Z. N.: Chaos, solitons & fractals, Chaos, solitons & fractals 29, 862 (2006)
[11] Narita, K.: Chaos, solitons & fractals, Chaos, solitons & fractals 3, 279 (1993)
[12] Christodoulides, D. N.; Joseph, R. J.: Opt lett, Opt lett 193, 794 (1988)
[13] Kevrekidis, P. G.; Rasmussen, K. O.; Bishop, A. R.: Int J mod phys B, Int J mod phys B 15, 2833 (2001)
[14] Scott, A. C.; Macneil, L.: Phys lett A, Phys lett A 98, 87 (1983)
[15] Su, W. P.; Schrieffer, J. R.; Heeger, A. J.: Phys rev lett, Phys rev lett 42, 1698 (1979)
[16] Marquii, P.; Bilbaut, J. M.; Remoissenet, M.: Phys rev E, Phys rev E 51, 6127 (1995)
[17] Eisenberg, H.; Silberberg, Y.; Moraudotti, R.; Boyd, A.; Aitchison, J.: Phys rev lett, Phys rev lett 81, 3383 (1998)
[18] Trombettoni, A.; Smerzi, A.: Phys rev lett, Phys rev lett 86, 2353 (2001)
[19] Wadati, M.; Toda, M.: J phy soc jpn, J phy soc jpn 39, 1196 (1975)
[20] Deng, S. F.; Chen, D. Y.: Chaos, solitons & fractals, Chaos, solitons & fractals 23, 1169 (2005)
[21] Hirota, R.; Hu, X. B.; Tang, X. Y.: J math anal appl, J math anal appl 288, 326 (2003)
[22] Hu, X. B.; Wu, Y. T.: Phys lett A, Phys lett A 246, 523 (1998)
[23] Man&uml, Manuel; As; Doliwa, Adam; Paolo, Maria Santini: Phys lett A, Phys lett A 232, 99 (1997)
[24] Qian, X. M.; Lou, S. L.; Hu, X. B.: J phys A math gen, J phys A math gen 37, 2401 (2003)
[25] Baldwin, D.; Göktas, Ü; Hereman, W.: Comput phys commun, Comput phys commun 162, 203 (2004)
[26] Dai, C. Q.; Yang, Q.; Zhang, J. F.: Z naturforsch, Z naturforsch 59a, 1 (2004)
[27] Xie, F. D.; Lu, Z. S.; Wang, D. K.: Chaos, solitons & fractals, Chaos, solitons & fractals 27, 217 (2006)
[28] Yan, Z. Y.: Nonlinear anal, Nonlinear anal 64, 1798 (2006)
[29] Yang, Z. H.; Hon, Y. C.: Chaos, solitons & fractals, Chaos, solitons & fractals 33, 1694 (2007)
[30] Wang, Q.; Yu, Y. X.: Chaos, solitons & fractals, Chaos, solitons & fractals 29, 904 (2006)
[31] Xie, F. D.; Wang, J. Q.: Chaos, solitons & fractals, Chaos, solitons & fractals 27, 1067 (2006)
[32] Lai, X. J.; Zhang, J. F.: Z naturforsch, Z naturforsch 60a, 573 (2005)
[33] Dai, C. Q.; Meng, J. P.; Zhang, J. F.: Commun theor phys, Commun theor phys 43, 471 (2005)
[34] Zhu, J. M.; Ma, Z. Y.: Chin phys, Chin phys 14, 17 (2005)
[35] Dai, C. Q.; Zhang, J. F.: Chaos, solitons & fractals, Chaos, solitons & fractals 27, 1042 (2006)
[36] Lü, D. Z.: Chaos, solitons & fractals, Chaos, solitons & fractals 24, 1373 (2005)
[37] Ablowitz, M. J.; Ladik, J. F.: Stud appl math, Stud appl math 55, 213 (1977)
[38] Quispel, G. R. W.; Nijhoff, F. W.; Capel, H. W.; Vander Linden, J.: Physica A, Physica A 125, 344 (1984)
[39] Dayydov, A.: J theor biol, J theor biol 38, 559 (1973)
[40] Takeno, S.; Hori, G.: J phys soc jpn, J phys soc jpn 60, 947 (1991)
[41] Aceves, A.; Angelis, C.; Luther, G.; Rubenchik, G.; Turitsyn, S.: Phys rev lett, Phys rev lett 75, 73 (1995)