Research PapersNo Access

ANALYTICAL INVESTIGATION OF THE CAUDREY–DODD–GIBBON–KOTERA–SAWADA EQUATION USING SYMBOLIC COMPUTATION

XIAO-GE XU

Beijing Information Science and Technology University, Beijing 100192, P. R. China

School of Science, Beijing University of Aeronautics and Astronautics, Beijing 100083, P. R. China

Corresponding author.

Search for more papers by this author

XIANG-HUA MENG

Beijing Information Science and Technology University, Beijing 100192, P. R. China

Search for more papers by this author

CHUN-YI ZHANG

Ministry-of-Education, Key Laboratory of Fluid Mechanics and National Laboratory for Computational Fluid Dynamics, Beijing University of Aeronautics and Astronautics, Beijing 100083, P. R. China

Search for more papers by this author

, and

YI-TIAN GAO

Ministry-of-Education, Key Laboratory of Fluid Mechanics and National Laboratory for Computational Fluid Dynamics, Beijing University of Aeronautics and Astronautics, Beijing 100083, P. R. China

State Key Laboratory of Software Development Environment, Beijing University of Aeronautics and Astronautics, Beijing 100083, P. R. China

Search for more papers by this author

https://doi.org/10.1142/S021797921250124XCited by:5 (Source: Crossref)

Abstract

In this paper, the Caudrey–Dodd–Gibbon–Kotera–Sawada (CDGKS) equation is analytically investigated using the Hirota bilinear method. Based on the bilinear form of the CDGKS equation, its N-soliton solution in explicit form is derived with the aid of symbolic computation. Besides the soliton solutions, several integrable properties such as the Bäcklund transformation, the Lax pair and the nonlinear superposition formula are also derived for the CDGKS equation.

Keywords:

You currently do not have access to the full text article.
Recommend the journal to your library today!

References

M. P. Barnettet al., Int. J. Quantum Chem. 100, 80 (2004), DOI: 10.1002/qua.20097. Web of Science, Google Scholar
B. Tian and Y. T. Gao, Eur. Phys. J. D 33, 59 (2005), DOI: 10.1140/epjd/e2005-00036-6. Web of Science, ADS, Google Scholar
B. Tian and Y. T. Gao, Eur. Phys. J. D 359, 241 (2006). Google Scholar
W. X. Ma, H. Y. Wu and J. S. He, Phys. Lett. A 364, 29 (2007), DOI: 10.1016/j.physleta.2006.11.048. Web of Science, ADS, Google Scholar
G. Das and J. Sarma, Phys. Plasmas 6, 4394 (1999), DOI: 10.1063/1.873705. Web of Science, ADS, Google Scholar
Z. Y. Yan and H. Q. Zhang, J. Phys. A 34, 1785 (2001), DOI: 10.1088/0305-4470/34/8/320. ADS, Google Scholar
Y. T. Gao and B. Tian, Phys. Plasmas Lett. 13, 120703 (2006), DOI: 10.1063/1.2402916. Web of Science, Google Scholar
Y. T. Gao and B. Tian, Europhys. Lett. 77, 15001 (2007), DOI: 10.1209/0295-5075/77/15001. Google Scholar
W. P. Hong, Phys. Lett. A 361, 520 (2007), DOI: 10.1016/j.physleta.2006.11.021. Web of Science, ADS, Google Scholar
B. Tianet al., Eur. Phys. J. B (Rapid Not.) 47, 329 (2005), DOI: 10.1140/epjb/e2005-00348-3. Web of Science, ADS, Google Scholar
B. Tianet al., Phys. Lett. A 356, 8 (2006), DOI: 10.1016/j.physleta.2006.03.080. Web of Science, ADS, Google Scholar
C. S. Gardneret al., Phys. Rev. Lett. 19, 1095 (1967), DOI: 10.1103/PhysRevLett.19.1095. Web of Science, Google Scholar
J. Weiss, M. Tabor and G. Carnevale, J. Math. Phys. 24, 522 (1983), DOI: 10.1063/1.525721. Web of Science, ADS, Google Scholar
F. Cariello and M. Tabor, Physica D 53, 59 (1991), DOI: 10.1016/0167-2789(91)90164-5. Web of Science, ADS, Google Scholar
W. X. Ma, J. Fudan Uni. (Nat. Sci.) 33, 319 (1994). Google Scholar
V. B. Matveev and M. A. Salle , Darboux Transformations and Solitons ( Springer , Berlin , 1991 ) . Google Scholar
W. X. Ma, Lett. Math. Phys. 39, 33 (1997), DOI: 10.1007/s11005-997-3049-3. Web of Science, ADS, Google Scholar
C. Rogers and W. R. Shadwick , Bäcklund Transformations and their Applications ( Academic Press , New York , 1982 ) . Google Scholar
R. Hirora, Phys. Rev. Lett. 27, 1192 (1971). Web of Science, ADS, Google Scholar
W. X. Ma and D. T. Zhou, Acta Phys. Sinica 42, 1731 (1993). Google Scholar
W. X. Ma and D. T. Zhou, Acta Math. Sci. (Supp.) 17, 168 (1997). Google Scholar
B. Tian and Y. T. Gao, Eur. Phys. J. B 22, 351 (2001). ADS, Google Scholar
E. G. Fan, Phys. Lett. A 277, 212 (2000), DOI: 10.1016/S0375-9601(00)00725-8. Web of Science, ADS, Google Scholar
J. M. Dye and A. Parker, J. Math. Phys. 43, 4921 (2002), DOI: 10.1063/1.1503866. Web of Science, ADS, Google Scholar
R. Hirota, X. B. Hu and X. Y. Tang, J. Math. Appl. 288, 326 (2003). Google Scholar
Y. Zhang and D. Y. Chen, Chaos Solit. Fract. 23, 175 (2005), DOI: 10.1016/j.chaos.2004.04.006. Web of Science, ADS, Google Scholar
Y. Zhang, D. Y. Chen and Z. B. Li, Chaos Solit. Fract. 29, 1188 (2006), DOI: 10.1016/j.chaos.2005.08.085. Web of Science, ADS, Google Scholar
W. X. Ma, Phys. Lett. A 301, 35 (2002), DOI: 10.1016/S0375-9601(02)00971-4. Web of Science, ADS, Google Scholar
W. X. Ma and Y. C. You, Trans. Am. Math. Soc. 357, 1753 (2005), DOI: 10.1090/S0002-9947-04-03726-2. Web of Science, Google Scholar
C. X. Liet al., Inverse Prob. 23, 279 (2007), DOI: 10.1088/0266-5611/23/1/015. Web of Science, ADS, Google Scholar
W. X. Ma and Y. C. You, Chaos Solit. Fract. 22, 395 (2004), DOI: 10.1016/j.chaos.2004.02.011. Web of Science, ADS, Google Scholar
W. X. Ma, Chaos Solit. Fract. 19, 163 (2004), DOI: 10.1016/S0960-0779(03)00087-0. Web of Science, ADS, Google Scholar
W. X. Ma, R. K. Bullough and P. J. Caudrey, J. Non. Math. Phys. 4, 293 (1997), DOI: 10.2991/jnmp.1997.4.3-4.6. Web of Science, Google Scholar
W. X. Ma and W. Strampp, Phys. Lett. A 341, 441 (2005), DOI: 10.1016/j.physleta.2005.05.013. Web of Science, ADS, Google Scholar
L. Eisenhart , A Treatise on the Differential Geometry of Curves and Surfaces ( Dover , New York , 1960 ) . Google Scholar
M. Wadati, H. Sanuki and K. Konno, Progr. Theor. Phys. 53, 419 (1975), DOI: 10.1143/PTP.53.419. Web of Science, ADS, Google Scholar
R. Hirota and J. Satsuma, J. Phys. Soc. Jpn. 45, 1741 (1978), DOI: 10.1143/JPSJ.45.1741. ADS, Google Scholar
K. Sawada and T. Kotera, Prog. Theor. Phys. 51, 1355 (1974), DOI: 10.1143/PTP.51.1355. Web of Science, ADS, Google Scholar
P. J. Caudrey, R. K. Dodd and J. D. Gibbon, Proc. R. Soc. Lond. A 351, 407 (1976). Web of Science, ADS, Google Scholar
J. Satsuma and D. J. Kaup, J. Phys. Soc. Jpn. 43, 692 (1977), DOI: 10.1143/JPSJ.43.692. ADS, Google Scholar
M. Nucci, Pseudopotentials, J. Phys. A: Math. Gen. 21, 73 (1988), DOI: 10.1088/0305-4470/21/1/016. Web of Science, ADS, Google Scholar
B. Fuchssteiner and W. Oevel, J. Math. Phys. 23, 358 (1982), DOI: 10.1063/1.525376. Web of Science, ADS, Google Scholar
S. Leble and N. Ustinov, Inverse Prob. 10, 617 (1994), DOI: 10.1088/0266-5611/10/3/008. Web of Science, ADS, Google Scholar
Y. Ohtaet al., Prog. Theor. Phys. Suppl. 94, 210 (1988), DOI: 10.1143/PTPS.94.210. ADS, Google Scholar
C. Gilson and J. Nimmo, Phys. Lett. A 47, 472 (1990). Google Scholar
Y. Cheng and Y. S. Li, J. Phys. A 25, 419 (1992), DOI: 10.1088/0305-4470/25/2/022. ADS, Google Scholar
R. Hirota , The Direct Method in Soliton Theory ( Cambrige University Press , Cambrige , 2004 ) . Google Scholar