Chin. Phys. Lett.  2008, Vol. 25 Issue (5): 1599-1602    DOI:
Original Articles |
Painleve Property and New Analytic Solutions for a Variable-Coefficient Kadomtsev--Petviashvili Equation with Symbolic Computation
WEI Guang-Mei1; GAO Yi-Tian2,3;XU Tao4;MENG Xiang-Hua4;ZHANG Chun-Yi5
1Department of Mathematics and LMIB, Beijing University of Aeronautics and Astronautics, Beijing 1000832Ministry-of-Education Key Laboratory of Fluid Mechanics and National Laboratory for Computational Fluid Dynamics, Beijing University of Aeronautics and Astronautics, Beijing 1000833State Key Laboratory of Software Development Environment, Beijing University of Aeronautics and Astronautics, Beijing 1000834School of Science, PO Box 122, Beijing University of Posts and Telecommunications, Beijing 1008765Meteorology Center of Air Force Command Post, Changchun 130051
Cite this article:   
WEI Guang-Mei, GAO Yi-Tian, XU Tao et al  2008 Chin. Phys. Lett. 25 1599-1602
Download: PDF(1839KB)  
Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks
Abstract A variable-coefficient Kadomtsev--Petviashvili equation is investigated. The Painleve analysis leads to its explicit Painleve-integrable conditions. An auto-Backlund transformation and the bilinear form are presented via the truncated Painleve expansion and symbolic computation. Several families of new analytic
solutions are presented, including the soliton-like and periodic solutions.
Keywords: 05.45.Yv      02.30.Jr      92.10.Hm      52.35.Mw      02.70.Wz     
Received: 05 February 2008      Published: 29 April 2008
PACS:  05.45.Yv (Solitons)  
  02.30.Jr (Partial differential equations)  
  92.10.Hm (Ocean waves and oscillations)  
  52.35.Mw (Nonlinear phenomena: waves, wave propagation, and other interactions (including parametric effects, mode coupling, ponderomotive effects, etc.))  
  02.70.Wz (Symbolic computation (computer algebra))  
TRENDMD:   
URL:  
https://cpl.iphy.ac.cn/       OR      https://cpl.iphy.ac.cn/Y2008/V25/I5/01599
Service
E-mail this article
E-mail Alert
RSS
Articles by authors
WEI Guang-Mei
GAO Yi-Tian
XU Tao
MENG Xiang-Hua
ZHANG Chun-Yi
[1] Ablowitz M J and Clarkson P A 1991 Solitons,Nonlinear Evolution Equations and Inverse Scattering (Cambridge:Cambridge University Press)
[2] Weiss J, Tabor M and Carnevale G 1983 J. Math.Phys. 24 522
[3] Hirota R 2004 The Direct Method in Soliton Theory(Cambridge: Cambridge University Press) Li Y S 1999 Solitons and Integrable Systems (Shanghai:Shanghai Scientific and Technological Education Publishing House) (in Chinese)
[4] Tian B, Wei G M, Zhang C Y, Shan W R and Gao Y T 2006 Phys. Lett. A 356 8 Wei G M, Gao Y T, Hu W and Zhang C Y 2006 Eur. Phys. J. B 53 343
[5] Ei G A and Grimshaw R H J 2002 Chaos 12 1015 Dcmiray H 2004 Int. J. Engng. Sci. 42 203 Tian B and Gao Y T 2005 Phys. Plasmas 12 054701 Li J, Xu T, Meng X H, Yang Z C, Zhu H W and Tian B 2007 Phys. Scr. 75 278
[6] Barnett M, Capitani J, Von Zur Gathen J and Gerhard J 2004 Int. J. Quantum Chem. 100 80 Hong W P 2007 Phys. Lett. A 361 520 Gao Y T and Tian B 2006 Phys. Plasmas 13 L120703 Gao Y T and Tian B 2007 Europhys. Lett. 77 15001 Tian B and Gao Y T 2007 Phys. Lett. A 362 283
[7] Tian J P, Li J H, Kang L S and Zhou G S 2005 PhysicaScripta 72 394 Li J, Zhang H Q, Xu T, Zhang Y X and Tian B 2007 J. Phys. A 40 13299 Li H and Wang D N 2007 Chin. Phys. Lett. 24 462 Tian B, Gao Y T and Zhu H W 2007 Phys. Lett. A 366 223
[8] Gwinn A W 1997 J. Fluid Mech. 341 195
[9] Milewski P 1998 J. Phys. D 123 36
[10] David D, Levi D and Winternitz P 1987 Stud. Appl.Math. 76 133 David D, Levi D and Winternitz P 1989 Stud. Appl. Math. 80 1
[11] Gungor F and Winternitz P 2002 J. Math.Anal. Appl. 276 314
[12] Ramani A, Grammaticos B and Bountis T 1989 Phys. Rep. 180 159
[13] Steeb E H and Euler N 1988 Nonlinear EvolutionEquations and the Painlev\'{e Test (Singapore: World Scientific)
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): 1599-1602
[2] WU Yong-Qi. Exact Solutions to a Toda-Like Lattice Equation in 2+1 Dimensions[J]. Chin. Phys. Lett., 2012, 29(6): 1599-1602
[3] HE Jing-Song, WANG You-Ying, LI Lin-Jing. Non-Rational Rogue Waves Induced by Inhomogeneity[J]. Chin. Phys. Lett., 2012, 29(6): 1599-1602
[4] YANG Zheng-Ping, ZHONG Wei-Ping. Self-Trapping of Three-Dimensional Spatiotemporal Solitary Waves in Self-Focusing Kerr Media[J]. Chin. Phys. Lett., 2012, 29(6): 1599-1602
[5] 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): 1599-1602
[6] S. Hussain. The Effect of Spectral Index Parameter κ on Obliquely Propagating Solitary Wave Structures in Magneto-Rotating Plasmas[J]. Chin. Phys. Lett., 2012, 29(6): 1599-1602
[7] CAO Ce-Wen**,ZHANG Guang-Yao. Lax Pairs for Discrete Integrable Equations via Darboux Transformations[J]. Chin. Phys. Lett., 2012, 29(5): 1599-1602
[8] YAN Jia-Ren**,ZHOU Jie,AO Sheng-Mei. The Dynamics of a Bright–Bright Vector Soliton in Bose–Einstein Condensation[J]. Chin. Phys. Lett., 2012, 29(5): 1599-1602
[9] 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): 1599-1602
[10] 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): 1599-1602
[11] S. Karimi Vanani, F. Soleymani. Application of the Homotopy Perturbation Method to the Burgers Equation with Delay[J]. Chin. Phys. Lett., 2012, 29(3): 1599-1602
[12] Saliou Youssoufa, Victor K. Kuetche, Timoleon C. Kofane. Generation of a New Coupled Ultra-Short Pulse System from a Group Theoretical Viewpoint: the Cartan Ehresman Connection[J]. Chin. Phys. Lett., 2012, 29(2): 1599-1602
[13] Hermann T. Tchokouansi, Victor K. Kuetche, Abbagari Souleymanou, Thomas B. Bouetou, Timoleon C. Kofane. Generating a New Higher-Dimensional Ultra-Short Pulse System: Lie-Algebra Valued Connection and Hidden Structural Symmetries[J]. Chin. Phys. Lett., 2012, 29(2): 1599-1602
[14] LIU Ping**, FU Pei-Kai. Note on the Lax Pair of a Coupled Hybrid System[J]. Chin. Phys. Lett., 2012, 29(1): 1599-1602
[15] GE Zhe-Yi, YIN Yan**, CHEN De-Peng, ZHUO Hong-Bin, MA Yan-Yun, SHAO Fu-Qiu. Stimulated Raman Backscattering Amplification Using Multiple Pump Pulses[J]. Chin. Phys. Lett., 2012, 29(1): 1599-1602
Viewed
Full text


Abstract