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TRAVELLING WAVE SOLUTIONS TO THE COUPLED DISCRETE NONLINEAR SCHRÖDINGER EQUATIONS

CHAO-QING DAI

Institute of Nonlinear Physics, Zhejiang Normal University, Jinhua 321004, China

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and

JIE-FANG ZHANG

Institute of Nonlinear Physics, Zhejiang Normal University, Jinhua 321004, China

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https://doi.org/10.1142/S0217979205029778Cited by:32 (Source: Crossref)

Abstract

In this paper, we have utilized the extended Jacobian elliptic function approach to construct seven families of new Jacobian elliptic function solutions for the coupled discrete nonlinear Schrödinger equations. When the modulus m → 1 or 0, some of these obtained solutions degenerate to the soliton solutions (the moving bright-bright and dark-dark solitons), the solitonic solutions and the trigonometric function solutions. This integrable model possesses the moving solitons because there is no PN barrier to block their motion in the lattice. We also find that some solutions in differential-difference equations (DDEs) are essentially identical to the continuous cases, while some solutions such as sec-type and tan-type in differential-difference models present different properties.

Keywords:

PACS: 05.45.Yv, 02.30.Jr, 02.30.Ik

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References

S. Flach and C. R. Willis, Phys. Rep. 295, 181 (1998); P. G. Kevrekidid, K. O. Rnsmussen and A. R. Bishop, Int. J. Mod. Phys. B15, 2833 (2001) . Google Scholar
A. C. Scott and L. Macheil, Phys. Lett. A98, 87 (1983); A. J. Sievers and S. Takeno, Phys. Rev. Lett. 61, 970 (1988) . Google Scholar
W. P. Su, J. R. Schrieffer and A. J. Heeger, Phys. Rev. Lett. 42, 1698 (1979). Crossref, Web of Science, ADS, Google Scholar
A. S. Davydov, J. Theor. Biol. 38, 599 (1973). Web of Science, Google Scholar
P. Marquii, J. M. Bilbault and M. Rernoissnet, Phys. Rev. E51, 6127 (1995). ADS, Google Scholar
A. Trombettoni and A. Smerzi, Phys. Rev. Lett. 86, 2353 (2001). Crossref, Web of Science, ADS, Google Scholar
H. Eisenberg, Y. Silberberg, R. Moraudotti, A. Boyd and J. Aitchison, Phys. Rev. Lett. 81, 3383 (1998); R. Morandotti, U. Peschel, J. Aitchison, H. Eisenberg and Y. Silberberg, ibid. 83, 2726 (1999) . Google Scholar
D. N. Christodoulides and N. K. Efremidis, Opt. Lett. 27, 568 (2002). Crossref, Web of Science, ADS, Google Scholar
M. Ablowitzet al., Phys. Rev. E65, 026602 (2002). Google Scholar
T. Peschel, U. Peschel and F. Ledever, Phys. Rev. E57, 1127 (1998). ADS, Google Scholar
C. S. Cardner, J. M. Kruskal and R. M. Miura, Phys. Rev. Lett. 19, 1095 (1967). Crossref, Web of Science, Google Scholar
H. D. Wahlquist and F. B. Estabrook, Phys. Lett. 31, 1386 (1971). Crossref, Web of Science, Google Scholar
J. F. Zhanget al., Chin. Phys. Lett. 20, 448 (2003). Web of Science, ADS, Google Scholar
E. G. Fan, Phys. Lett. A282, 18 (2001). ADS, Google Scholar
E. G. Parkes, B. R. Duffy and P. C. Abbott, Phys. Lett. A295, 280 (2002). ADS, Google Scholar
X. M. Qian, S. Y. Lou and X. B. Hu, J. Phys. A: Math 37, 2401 (2003); X. M. Qian, S. Y. Lou and X. B. Hu, Znaturforsch 59A, 645 (2004) . Google Scholar
D. Baldwin, Ü. Göktas and W. Hereman, Comput. Phys. Commun. 162, 203 (2004). Crossref, Web of Science, ADS, Google Scholar
C. Q. Dai, Q. Yang and J. F. Zhang, Znaturforsch 59A, 635 (2004). ADS, Google Scholar
K. Narita, J. Phys. Soc. Jpn. 66, 2207 (1997). Crossref, ADS, Google Scholar
M. Ablowitz and J. F. Ladik, Stud. Appl. Math. 55, 213 (1976). Crossref, Web of Science, Google Scholar
A. Davydov, J. Theor. Biol. 38, 559 (1973). Crossref, Web of Science, ADS, Google Scholar
S. Takeno and G. Hori, J. Phys. Soc. Jpn. 60, 947 (1991). Crossref, ADS, Google Scholar
A. Aceveset al., Phys. Rev. Lett. 75, 73 (1995). Crossref, Web of Science, ADS, Google Scholar
Z. Y. Yan, Comput. Phys. Commun. 148, 30 (2002). Crossref, Web of Science, ADS, Google Scholar
A. V. Buryak, Y. S. Kivshar and D. F. Parker, Phys. Lett. A215, 57 (1996). ADS, Google Scholar
M. J. Ablowitz and D. J. Benney, Stud. Appl. Math 49, 225 (1970); G. P. Agrawal, Phys. Rev. Lett. 59, 880 (1987); C. J. Mckindtrie and R. Bingham, Phys. Fluids B1, 230 (1989); C. R. Menyuk, IEEE J. Quantum Electron 25, 2674 (1989); N. M. Ryskin, JETP 79, 833 (1994) . Google Scholar
M. Haelterman and A. P. Sheppard, Phys. Rev. E49, 3389 (1994); Yu. S. Kivshar and S. K. Turitsyn, Opt. Lett. 18, 337 (1993) . Google Scholar
S. V. Manakov, Zh. Eksp. Teor. Fiz. 65, 505 (1973); Sov. Phys. JETP 38, 248 (1974); M. Karlsson, D. J. Kaup and B. A. Malomed, Phys. Rev. E54, 5802 (1996) . Google Scholar
B. A. Malomed and J. K. Yang, Phys. Lett. A302, 163 (2002). ADS, Google Scholar
T. Dauxois and M. Peyrard, Phys. Rev. Lett. 70, 3935 (1993). Crossref, Web of Science, ADS, Google Scholar
O. O. Vakhnenko and V. O. Vakhnenko, Phys. Lett. A196, 307 (1995). ADS, Google Scholar
Y. S. Kivshar and D. K. Campbell, Phys. Rev. E48, 3077 (1993). ADS, Google Scholar
A. Bülow, D. Henning and H. Gabriel, Phys. Rev. E59, 2380 (1999). ADS, Google Scholar