Chin. Phys. Lett.  2008, Vol. 25 Issue (8): 2739-2742    DOI:
Original Articles |
Periodic Wave Solution to the (3+1)-Dimensional Boussinesq Equation
WU Yong-Qi
Department of Mathematics, Zhanjiang Normal University, Zhanjiang 524048
Cite this article:   
WU Yong-Qi 2008 Chin. Phys. Lett. 25 2739-2742
Download: PDF(204KB)  
Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks
Abstract One- and two-periodic wave solutions for (3+1)-dimensional Boussinesq equation are presented by means of Hirota's bilinear method and the Riemann theta function. The soliton solution can be obtained from the periodic wave solution in an appropriate limiting procedure.
Keywords: 02.30.Jr     
Received: 14 January 2008      Published: 25 July 2008
PACS:  02.30.Jr (Partial differential equations)  
TRENDMD:   
URL:  
https://cpl.iphy.ac.cn/       OR      https://cpl.iphy.ac.cn/Y2008/V25/I8/02739
Service
E-mail this article
E-mail Alert
RSS
Articles by authors
WU Yong-Qi
[1] Ablowitz M J and Segur H 1981 Solitons and theInverse Scattering Transform (Philadelphia, PA: SIAM)
[2]Newell A C 1985 Solitons in Mathematics and Physics(Philadelphia, PA: SIAM)
[3]Novikov S, Manakov S V, Pitaevskii L P and Zakharov V E1984 Theory of Solitons, The Inverse Scattering Methods (NewYork: Consultants Bureau)
[4]Cherednik I 1996 Basic Methods of Soliton Theory(Singapore: World Scientific)
[5]Belokolos E D, Bobenko A I, Enolskii V Z, Its A R andMatveev V B 1994 Algebro-Geometric Approach to NonlinearIntegrable Equations Berlin: Springer
[6]Cao C W, Wu Y T and Geng X G 1999 J. Math. Phys. 40 3948
[7]Cao C W, Geng X G and Wu Y T 1999 J. Phys. A 328059
[8]Geng X G, Wu Y T and Cao C W 1999 J. Phys. A 323733
[9]Wang M L 1995 Phys. Lett. A 199 169
[10]Lei Y 1999 Phys. Lett. A 260 55
[11]Fan E G and Zhang H Q 1998 Acta Phys. Sin. 47353 (in Chinese)
[12]Fan E G 2000 Acta Phys. Sin. 49 1409 (inChinese)
[13]Parkes E J and Duffy B R 1997 Phys. Lett. A 229 217
[14]Fan E G 2000 Phys. Lett. A 277 212
[15]Zhang G X, Li Z B and Duan Y S 2000 Sci. Chin. A 30 1103 (in Chinese)
[16]Shi Y R, L\"{u K P, Duan W S and Zhao J B 2001 ActaPhys. Sin. 50 2074 (in Chinese)
[17]Guo G P and Zhang J F 2002 Acta Phys. Sin. 511159 (in Chinese)
[18]Liu S K, Fu Z T, Liu S D and Zhao Q 2001 Phys. Lett. A 289 69
[19]Fu Z T, Liu S K, Liu S D and Zhao Q 2001 Phys. Lett. A 290 72
[20]Zeng X and Zhang H Q 2005 Acta Phys. Sin. 541476 (in Chinese)
[21] Lin M M, Duan W S and L\"{u K P 2007 J. NorthwestNormal University(Natural Science) 43(1) 39 (in Chinese)
[22]Li M J and Jiu Q S 2007 Acta Math. Appl. Sin. 30 936 (in Chinese)
[23]Senthilvelan M 2001 Comput. Math. Appl. 123381
[24]Allen M A and Rowlands G 1997 Phys. Lett. A 235 145
[25]Chen Y, Yan Z Y and Zhang H Q 2003 Phys. Lett. A 307 107
[26]Matsuno Y 1984 Bilinear Transformation Method (NewYork: Academic)
[27] Farkas H M and Kra I 1992 Riemann Surfaces (Berlin:Springer)
Related articles from Frontiers Journals
[1] E. M. E. Zayed, S. A. Hoda Ibrahim. Exact Solutions of Nonlinear Evolution Equations in Mathematical Physics Using the Modified Simple Equation Method[J]. Chin. Phys. Lett., 2012, 29(6): 2739-2742
[2] WU Yong-Qi. Exact Solutions to a Toda-Like Lattice Equation in 2+1 Dimensions[J]. Chin. Phys. Lett., 2012, 29(6): 2739-2742
[3] CUI Kai. New Wronskian Form of the N-Soliton Solution to a (2+1)-Dimensional Breaking Soliton Equation[J]. Chin. Phys. Lett., 2012, 29(6): 2739-2742
[4] CAO Ce-Wen**,ZHANG Guang-Yao. Lax Pairs for Discrete Integrable Equations via Darboux Transformations[J]. Chin. Phys. Lett., 2012, 29(5): 2739-2742
[5] DAI Zheng-De**, WU Feng-Xia, LIU Jun and MU Gui. New Mechanical Feature of Two-Solitary Wave to the KdV Equation[J]. Chin. Phys. Lett., 2012, 29(4): 2739-2742
[6] Mohammad Najafi**,Maliheh Najafi,M. T. Darvishi. New Exact Solutions to the (2+1)-Dimensional Ablowitz–Kaup–Newell–Segur Equation: Modification of the Extended Homoclinic Test Approach[J]. Chin. Phys. Lett., 2012, 29(4): 2739-2742
[7] S. Karimi Vanani, F. Soleymani. Application of the Homotopy Perturbation Method to the Burgers Equation with Delay[J]. Chin. Phys. Lett., 2012, 29(3): 2739-2742
[8] LIU Ping**, FU Pei-Kai. Note on the Lax Pair of a Coupled Hybrid System[J]. Chin. Phys. Lett., 2012, 29(1): 2739-2742
[9] LOU Yan, ZHU Jun-Yi** . Coupled Nonlinear Schrödinger Equations and the Miura Transformation[J]. Chin. Phys. Lett., 2011, 28(9): 2739-2742
[10] A H Bokhari, F D Zaman, K Fakhar, *, A H Kara . A Note on the Invariance Properties and Conservation Laws of the Kadomstev–Petviashvili Equation with Power Law Nonlinearity[J]. Chin. Phys. Lett., 2011, 28(9): 2739-2742
[11] LI Dong **, XIE Zheng, YI Dong-Yun . Numerical Simulation of Hyperbolic Gradient Flow with Pressure[J]. Chin. Phys. Lett., 2011, 28(7): 2739-2742
[12] ZHAO Song-Lin**, ZHANG Da-Jun, CHEN Deng-Yuan . A Direct Linearization Method of the Non-Isospectral KdV Equation[J]. Chin. Phys. Lett., 2011, 28(6): 2739-2742
[13] WU Yong-Qi. Asymptotic Behavior of Periodic Wave Solution to the Hirota–Satsuma Equation[J]. Chin. Phys. Lett., 2011, 28(6): 2739-2742
[14] ZHAO Li-Yun, GUO Bo-Ling, HUANG Hai-Yang** . Blow-up Solutions to a Viscoelastic Fluid System and a Coupled Navier–Stokes/Phase-Field System in R2[J]. Chin. Phys. Lett., 2011, 28(6): 2739-2742
[15] WU Jian-Ping . Bilinear Bäcklund Transformation for a Variable-Coefficient Kadomtsev–Petviashvili Equation[J]. Chin. Phys. Lett., 2011, 28(6): 2739-2742
Viewed
Full text


Abstract