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)
Rational Jacobi elliptic solutions for nonlinear differential-difference lattice equations. (English) Zbl 1252.34013
Summary: We present a direct new method for constructing the rational Jacobi elliptic solutions for nonlinear differential-difference equations, which may be called the rational Jacobi elliptic function method. We use the rational Jacobi elliptic function method to construct many new exact solutions for some nonlinear differential-difference equations in mathematical physics via the lattice equation. The proposed method is effective for obtaining the exact solutions for nonlinear differential-difference equations.
34A33Lattice differential equations
34A05Methods of solution of ODE
[1]Fermi, E.; Pasta, J.; Ulam, S.: Collected papers of enrico Fermi II, (1965)
[2]Su, W. P.; Schrieffer, J. R.; Heeger, A. J.: Solitons in polyacetylene, Phys. rev. Lett. 42, 1698-1701 (1979)
[3]Davydov, A. S.: The theory of contraction of proteins under their excitation, J. theoret. Biol. 38, 559-569 (1973)
[4]Marquié, P.; Bilbault, J. M.; Remoissenet, M.: Observation of nonlinear localized modes in an electrical lattice, Phys. rev. E 51, 6127-6133 (1995)
[5]Toda, M.: Theory of nonlinear lattices, (1989)
[6]Wadati, M.: Transformation theories for nonlinear discrete systems, Prog. suppl. Theor. phys. 59, 36-63 (1976)
[7]Ohta, Y.; Hirota, R.: A discrete KdV equation and its Casorati determinant solution, J. phys. Soc. Japan 60, 2095 (1991)
[8]Ablowitz, M. J.; Ladik, J.: Nonlinear differential–difference equations, J. math. Phys. 16, 598-603 (1975) · Zbl 0296.34062 · doi:10.1063/1.522558
[9]Hu, X. B.; Ma, W. X.: Application of Hirota’s bilinear formalism to the Toeplitz lattice some special soliton-like solutions, Phys. lett. A 293, 161-165 (2002) · Zbl 0985.35072 · doi:10.1016/S0375-9601(01)00850-7
[10]Baldwin, D.; Goktas, U.; Hereman, W.: Symbolic computation of hyperbolic tangent solutions for nonlinear differential–difference equations, Comput. phys. Commun. 162, 203-217 (2004) · Zbl 1196.68324 · doi:10.1016/j.cpc.2004.07.002
[11]Liu, S. K.; Fu, Z. T.; Wang, Z. G.; Liu, S. D.: Periodic solutions for a class of nonlinear differential–difference equations, Commun. theor. Phys. 49, 1155-1158 (2008)
[12]Qiong, C.; Bin, L.: Application of Jacobi elliptic function expansion method for nonlinear difference equations, Commun. theor. Phys. 43, 385-388 (2005)
[13]Xie, F.; Jia, M.; Zhao, H.: Some solutions of discrete sine–Gordon equation, Chaos solitons fractals 33, 1791-1795 (2007) · Zbl 1129.35456 · doi:10.1016/j.chaos.2006.03.018
[14]Zhu, S. D.: Exp-function method for the hybrid-lattice system, Int. J. Nonlinear sci. 8, 461 (2007)
[15]Aslan, I.: A discrete generalization of the extended simplest equation method, Commun. nonlinear sci. Numer. simul. 15, 1967-1973 (2010) · Zbl 1222.65114 · doi:10.1016/j.cnsns.2009.08.008
[16]Yang, P.; Chen, Y.; Li, Z. B.: ADM–Padé technique for the nonlinear lattice equations, Appl. math. Comput. 210, 362-375 (2009) · Zbl 1162.65399 · doi:10.1016/j.amc.2009.01.010
[17]Zhu, S. D.; Chu, Y. M.; Qiu, S. L.: The homotopy perturbation method for discontinued problems arising in nanotechnology, Comput. math. Appl. 58 (2009) · Zbl 1189.65186 · doi:10.1016/j.camwa.2009.03.048
[18]Zhang, S.; Dong, L.; Ba, J.; Sun, Y.: The (G’/G)-expansion method for nonlinear differential–difference equations, Phys. lett. A 373, 905-910 (2009) · Zbl 1228.34096 · doi:10.1016/j.physleta.2009.01.018
[19]Aslan, I.: The Ablowitz–Ladik lattice system by means of the extended (G’/G)-expansion method, Appl. math. Comput. 216, 2778-2782 (2010) · Zbl 1193.35179 · doi:10.1016/j.amc.2010.03.124
[20]Zhang, S.: Discrete Jacobi elliptic function expansion method for nonlinear difference equation, Phys. scr. 80, 045002-045010 (2009) · Zbl 1179.35337 · doi:10.1088/0031-8949/80/04/045002
[21]Gepreel, Khaled A.: Rational Jacobi elliptic solutions for nonlinear difference differential equations, Nonlinear sci. Lett. A 2, 151-158 (2011)
[22]Wu, G.; Xia, T.: A new method for constructing soliton solutions to differential–difference equation with symbolic computation, Chaos solitons fractals 39, 2245-2248 (2009) · Zbl 1197.35250 · doi:10.1016/j.chaos.2007.06.107
[23]Xie, F.; Wang, J.: A new method for solving nonlinear differential–difference equation, Chaos solitons fractals 27, 1067-1071 (2006) · Zbl 1094.34058 · doi:10.1016/j.chaos.2005.04.078
[24]Liu, C.: Exponential function rational expansion method for nonlinear differential–difference equations, Chaos solitons fractals 40, 708-716 (2009) · Zbl 1197.35243 · doi:10.1016/j.chaos.2007.08.018
[25]Wang, Q.; Yu, Y.: New rational formal for (1+1)-dimensional Toda equation and another Toda equation, Chaos solitons fractals 29, 904-915 (2006) · Zbl 1142.37370 · doi:10.1016/j.chaos.2005.08.053