Non-autonomous discrete Boussinesq equation：Solutions and consistency

doi:10.1088/1674-1056/23/7/070202

Abstract A non-autonomous 3-component discrete Boussinesq equation is discussed. Its spacing parameters p_n and q_m are related to independent variables n and m, respectively. We derive bilinear form and solutions in Casoratian form. The plain wave factor is defined through the cubic roots of unity. The plain wave factor also leads to extended non-autonomous discrete Boussinesq equation which contains a parameter δ. Tree-dimendional consistency and Lax pair of the obtained equation are discussed.

Keywords: non-autonomous discrete Boussinesq equation bilinear solutions Lax pair

Received: 27 November 2013
Revised: 05 January 2014
Accepted manuscript online:

PACS:	02.30.Ik	(Integrable systems)
	05.45.Yv	(Solitons)

Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11071157 and 11371241), the Social Responsibility Foundation for the Doctoral Program of Higher Education of China (Grant No. 20113108110002), and the Project of "First-class Discipline of Universities in Shanghai" of China.

Corresponding Authors: Nong Li-Juan
E-mail: nonglijuan2008@163.com

About author: 02.30.Ik; 05.45.Yv

Cite this article:

Nong Li-Juan (农丽娟), Zhang Da-Juan (张大军) Non-autonomous discrete Boussinesq equation：Solutions and consistency 2014 Chin. Phys. B 23 070202

[1]	Nijhoff F W and Walker A J 2001 Glasgow Math. J. 43A 109
[2]	Nijhoff F W 2002 Phys. Lett. A 297 49
[3]	Bobenko A I and Suris Y B 2002 Int. Math. Res. Not. 11 573
[4]	Adler V E, Bobenko A I and Suris Yu B 2003 Commun. Math. Phys. 233 513
[5]	Hietarinta J 2011 J. Phys. A: Math. Theor. 44 165204
[6]	Grammaticos B and Ramani A 2010 Lett. Math. Phys. 92 33
[7]	Shi Y and Zhang D J 2012 arXiv:1201.6408[nonl.SI]
[8]	Hietarinta J and Zhang D J 2009 J. Phys. A: Math. Theor. 42 404006
[9]	Hietarinta J and Zhang D J 2011 SIGMA 7 061
[10]	Zhang D J, Zhao S L and Nijhoff F W 2012 Stud. Appl. Math. 129 220
[11]	Tongas A and Nijhoff F 2005 Glasgow Math. J. 47A 205
[12]	Hietarinta J and Zhang D J 2010 J. Phys. A: Math. Theor. 51 033505
[13]	Freeman N C and Nimmo J J C 1983 Phys. Lett. A 95 1
[14]	Nong L J, Zhang D J, Shi Y and Zhang W Y 2013 Chin. Phys. Lett. 30 040201
[15]	Hietarinta J and Viallet C 2012 Nonlinearity 25 1955
[16]	Atkinson J, Hietarinta J and Nijhoff F 2007 J. Phys. A: Math. Theor. 40 F1
[17]	Atkinson J, Hietarinta J and Nijhoff F 2008 J. Phys. A: Math. Theor. 41 142001
[18]	Grammaticos B, Ramani A and Papageorgiou V 1991 Phys. Rev. Lett. 67 1825
[19]	Hietarinta J 2005 J. Nonl. Math. Phys. 12 223
[20]	Kajiwara K and Mukaihira A 2005 J. Phys. A: Math. Gen. 38 6363
[21]	Kajiwara K and Ohta Y 2008 J. Phys. Soc. Jpn. 77 054004
[22]	Kajiwara K and Ohta Y 2009 RIMS Kôkyûroku Bessatsu B13 53
[23]	Nijhoff F, Papageorgiou V, Capel H and Quispel G 1992 Inv. Probl. 8 597
[24]	Nijhoff F 1999 Discrete Integrable Geometry and Physics (Oxford: Clarendon Press) p. 209
[25]	Papageorgiou V, Grammaticos B and Ramani A 1993 Phys. Lett. A 179 111
[26]	Sahadevan R, Rasinb O and Hydon P 2007 J. Math. Anal. Appl. 331 712
[27]	Walker A J 2001 Similarity Reductions and Integrable Lattice Equations (Ph.D. thesis) (Leeds: Leeds University)
[28]	Zhang D J 2006 Chin. Phys. Lett. 23 2349
[29]	Zhang D J, Ning T K, Bi J B and Chen D Y 2006 Phys. Lett. A 359 458
[30]	Zhang D J 2006 arXiv:nlin.SI/0603008[hep-ph]
[31]	Zhang D J and Hietarinta J 2010 Nonlinear and Modern Mathematical Physics: Proceedings of the First International Workshop, July 15-21, 2009 Beijing, China, pp. 154-161
[32]	Zhao S L, Zhang D J and Shi Y 2012 Chin. Ann. Math. 33B 259
[33]	Lou S Y, Li Y Q and Tang X Y 2013 Chin. Phys. Lett. 30 080202
[34]	Dong Z Z and Chen Y 2010 Commun. Theor. Phys. 54 389
[35]	Wang X, Chen Y and Dong Z Z 2014 Chin. Phys. B 23 010201

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