Search
This Journal
This Journal
Anywhere
Quick Search in Journals
Enter words / phrases / DOI / ISBN / keywords / authors / etc
Access type:Only show content I have full access toOnly show Open Access
Advanced Search
0 My Cart
Sign in
Institutional Access

System Upgrade on Tue, May 28th, 2024 at 2am (EDT)

Existing users will be able to log into the site and access content. However, E-commerce and registration of new users may not be available for up to 12 hours.
For online purchase, please visit us again. Contact us at customercare@wspc.com for any enquiries.

Research PapersNo Access

N-SOLITON-LIKE SOLUTIONS AND BÄCKLUND TRANSFORMATIONS FOR A NON-ISOSPECTRAL AND VARIABLE-COEFFICIENT MODIFIED KORTEWEG-DE VRIES EQUATION

Ministry-of-Education Key Laboratory of Fluid Mechanics and National Laboratory for Computational Fluid Dynamics, Beijing University of Aeronautics and Astronautics, Beijing 100191, China

Search for more papers by this author

,

Ministry-of-Education Key Laboratory of Fluid Mechanics and National Laboratory for Computational Fluid Dynamics, Beijing University of Aeronautics and Astronautics, Beijing 100191, China

State Key Laboratory of Software Development Environment, Beijing University of Aeronautics and Astronautics, Beijing 100191, China

Corresponding author.

Search for more papers by this author

,

School of Science, Beijing University of Posts and Telecommunications, P. O. Box 122, Beijing 100876, China

Search for more papers by this author

,

Ministry-of-Education Key Laboratory of Fluid Mechanics and National Laboratory for Computational Fluid Dynamics, Beijing University of Aeronautics and Astronautics, Beijing 100191, China

Search for more papers by this author

,

Ministry-of-Education Key Laboratory of Fluid Mechanics and National Laboratory for Computational Fluid Dynamics, Beijing University of Aeronautics and Astronautics, Beijing 100191, China

Search for more papers by this author

,

School of Science, Beijing University of Posts and Telecommunications, P. O. Box 122, Beijing 100876, China

Search for more papers by this author

, and

State Key Laboratory of Software Development Environment, Beijing University of Aeronautics and Astronautics, Beijing 100191, China

School of Science, Beijing University of Posts and Telecommunications, P. O. Box 122, Beijing 100876, China

Key Laboratory of Information Photonics and Optical Communications (BUPT), Ministry of Education, P.O. Box 128, Beijing University of Posts and Telecommunications, Beijing 100876, China

Search for more papers by this author

https://doi.org/10.1142/S0217979211058043Cited by:7 (Source: Crossref)

Abstract

A non-isospectral and variable-coefficient modified Korteweg–de Vries (mKdV) equation is investigated in this paper. Starting from the Ablowitz–Kaup–Newell–Segur procedure, the Lax pair is established and the Bäcklund transformation in original variables is also derived. By a dependent variable transformation, the non-isospectral and variable-coefficient mKdV equation is transformed into bilinear equations, by virtue of which the N-soliton-like solution is obtained. In addition, the bilinear Bäcklund transformation gives a one-soliton-like solution from a vacuum one. Furthermore, the N-soliton-like solution in the Wronskian form is constructed and verified via the Wronskian technique.

Keywords:

PACS: 05.45.Yv, 47.35.Fg, 02.30.Jr, 02.30.Ik, 02.70.Wz

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

References

W. X. Ma, R. K. Bullough and P. J. Caudrey, J. Nonl. Math. Phys. 4, 293 (1997). Crossref, Web of Science, Google Scholar
W. X. Ma and H. Y. Wu, J. Math. Anal. Appl. 324, 134 (2006). Crossref, Web of Science, Google Scholar
M. V. Bartuccelli and G. Gentile, Phys. Lett. A 307, 274 (2003), DOI: 10.1016/S0375-9601(02)01731-0. Crossref, Web of Science, ADS, Google Scholar
M. P. Barnettet al., Int. J. Quant. Chem. 100, 80 (2004), DOI: 10.1002/qua.20097. Crossref, Web of Science, Google Scholar
B. Tian and Y. T. Gao, Phys. Plasmas 12, 054701 (2005), DOI: 10.1063/1.1885477. Crossref, Web of Science, Google Scholar
B. Tian and Y. T. Gao, Phys. Lett. A 340, 243 (2005). Crossref, Web of Science, ADS, Google Scholar
B. Tian and Y. T. Gao, Phys. Lett. A 340, 449 (2005). Crossref, Web of Science, ADS, Google Scholar
B. Tian and Y. T. Gao, Phys. Lett. A 342, 228 (2005). Crossref, Web of Science, ADS, Google Scholar
B. Tian and Y. T. Gao, Phys. Lett. A 359, 241 (2007), DOI: 10.1016/j.physleta.2006.06.032. Crossref, Web of Science, ADS, Google Scholar
B. Tian and Y. T. Gao, Phys. Lett. A 362, 283 (2007). Crossref, Web of Science, ADS, Google Scholar
B. Tian, Y. T. Gao and H. W. Zhu, Phys. Lett. A 366, 223 (2007). Crossref, Web of Science, ADS, Google Scholar
G. Das and J. Sarma, Phys. Plasmas 6, 4394 (1999), DOI: 10.1063/1.873705. Crossref, Web of Science, ADS, Google Scholar
W. P. Hong, Phys. Lett. A 361, 520 (2007). Crossref, Web of Science, ADS, Google Scholar
Y. T. Gao and B. Tian, Phys. Plasmas 13, 112901 (2006), DOI: 10.1063/1.2363352. Crossref, Web of Science, Google Scholar
Y. T. Gao and B. Tian, Phys. Plasmas 13, 120703 (2007), DOI: 10.1063/1.2402916. Crossref, Web of Science, Google Scholar
Y. T. Gao and B. Tian, Phys. Lett. A 349, 314 (2007). Crossref, 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. Crossref, Web of Science, ADS, Google Scholar
B. Tian and Y. T. Gao, Phys. Plasmas 12, 070703 (2005), DOI: 10.1063/1.1950120. Crossref, 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. Crossref, Web of Science, ADS, Google Scholar
Y. T. Gao and B. Tian, Phys. Lett. A 361, 523 (2007). Crossref, Web of Science, ADS, Google Scholar
Y. T. Gao and B. Tian, Europhys. Lett. 77, 15001 (2007), DOI: 10.1209/0295-5075/77/15001. Crossref, Google Scholar
W. L. Chan and K. S. Li, J. Funct. Anal. 121, 426 (1994), DOI: 10.1006/jfan.1994.1055. Crossref, Web of Science, Google Scholar
G. F. Yu, J. Phys. A 39, 3367 (2006), DOI: 10.1088/0305-4470/39/13/014. Crossref, ADS, Google Scholar
S. F. Deng, D. J. Zhang and D. Y. Chen, J. Phys. Soc. Jpn. 74, 2383 (2005), DOI: 10.1143/JPSJ.74.2383. Crossref, ADS, Google Scholar
Y. Zhang and Y. N. Lv, J. Math. Anal. Appl. 342, 534 (2008). Crossref, Web of Science, Google Scholar
B. Tianet al., Phys. Lett. A 356, 8 (2006). Crossref, Web of Science, ADS, Google Scholar
T. Xuet al., Wave Motion 44, 262 (2007), DOI: 10.1016/j.wavemoti.2006.10.004. Crossref, Web of Science, ADS, Google Scholar
R. Y. Haoet al., Opt. Commun. 236, 79 (2004), DOI: 10.1016/j.optcom.2004.03.005. Crossref, Web of Science, ADS, Google Scholar
W. X. Ma, Phys. Lett. A 179, 179 (1993), DOI: 10.1016/0375-9601(93)91135-R. Crossref, Web of Science, ADS, Google Scholar
T. Xuet al., Phys. Lett. A 372, 1990 (2008), DOI: 10.1016/j.physleta.2008.04.055. Crossref, Web of Science, Google Scholar
Z. Y. Yan, Phys. Lett. A 372, 969 (2008). Crossref, Web of Science, ADS, Google Scholar
W. Ames , Nonlinear Partial Differential Equations ( Academic Press , New York , 1967 ) . Google Scholar
T. I. Karpman and H. Ono, J. Phys. Soc. Jpn. 34, 1073 (1973). Google Scholar
H. Ono, J. Phys. Soc. Jpn. 61, 4336 (1992), DOI: 10.1143/JPSJ.61.4336. Crossref, ADS, Google Scholar
T. S. Komatsu and S. I. Sasa, Phys. Rev. E 52, 5574 (1995), DOI: 10.1103/PhysRevE.52.5574. Crossref, Web of Science, ADS, Google Scholar
K. E. Lonngren, Opt. Quant. Electron. 30, 615 (1998), DOI: 10.1023/A:1006910004292. Crossref, Web of Science, Google Scholar
A. H. Khater, O. H. EI-Kalaawy and D. K. Callebaut, Phys. Scr. 58, 545 (1998), DOI: 10.1088/0031-8949/58/6/001. Crossref, Web of Science, ADS, Google Scholar
V. Ziegler, Chaos Solit. Fract. 12, 1719 (2001), DOI: 10.1016/S0960-0779(00)00137-5. Crossref, Web of Science, ADS, Google Scholar
S. Biswajit and R. Rajkumar, Phys. Plasmas 10, 10 (2003). Google Scholar
L. X. Tian, Appl. Math. Mech. 15, 539 (1994). Web of Science, Google Scholar
S. Y. Lou and H. Y. Ruan, Acta. Phys. Sin. 41, 182 (1992). Web of Science, Google Scholar
M. J. Ablowtiz and P. A. Clarkson , Soliton, Nonlinear Evolution Equations and Inverse Scattering ( Cambridge University Press , Cambridge , 1991 ) . Crossref, Google Scholar
C. H. Gu et al. , Soliton Theory and Its Application ( Springer-Verlag , Berlin , 1995 ) . Crossref, Google Scholar
Z. Y. Yan, Commun. Nonl. Sci. Numer. Simul. 4, 284 (1999), DOI: 10.1016/S1007-5704(99)90043-6. Crossref, Google Scholar
S. Zhang, J. L. Tong and W. Wang, Phys. Lett. A 372, 2254 (2008), DOI: 10.1016/j.physleta.2007.11.026. Crossref, Web of Science, ADS, Google Scholar
D. S. Li and H. Q. Zhang, Acta. Phys. Sin. 52, 7 (2003). Google Scholar
C. Q. Dai, J. M. Zhu and J. F. Zhang, Chaos Solit. Fract. 27, 881 (2006), DOI: 10.1016/j.chaos.2005.04.072. Crossref, Web of Science, ADS, Google Scholar
S. Zhang and T. C. Xia, Phys. Lett. A 372, 1741 (2008). Crossref, Web of Science, ADS, Google Scholar
R. Hirota, Phys. Rev. Lett. 27, 1192 (1971), DOI: 10.1103/PhysRevLett.27.1192. Crossref, Web of Science, ADS, Google Scholar
R. Hirota , The Direct Method in Soliton Theory ( Cambridge University Press , Cambridge , 2004 ) . Crossref, Google Scholar
J. Satsuma, J. Phys. Soc. Jpn. 40, 286 (1976), DOI: 10.1143/JPSJ.40.286. Crossref, ADS, Google Scholar
M. J. Ablowitzet al., Phys. Rev. Lett. 31, 125 (1973), DOI: 10.1103/PhysRevLett.31.125. Crossref, Web of Science, ADS, Google Scholar
M. J. Ablowitzet al., Stud. Appl. Math. 53, 249 (1974). Crossref, Web of Science, Google Scholar
S. F. Deng, Phys. Lett. A 362, 198 (2007). Crossref, Web of Science, ADS, Google Scholar
G. G. Yu and H. W. Tam, J. Phys. A 39, 3367 (2006), DOI: 10.1088/0305-4470/39/13/014. Crossref, ADS, Google Scholar
X. H. Menget al., Z. Naturforsch. A 62, 13 (2007). Crossref, Web of Science, ADS, Google Scholar
J. Liet al., J. Math. Anal. Appl. 336, 1443 (2007). Crossref, Web of Science, Google Scholar
X. H. Menget al., Physica A 387, 97 (2008). Crossref, Web of Science, ADS, Google Scholar
K. Konno and M. Wadati, Prog. Theor. Phys. 53, 1652 (1975), DOI: 10.1143/PTP.53.1652. Crossref, Web of Science, ADS, Google Scholar
N. C. Freeman and J. J. C. Nimmo, Phys. Lett. A 95, 1 (1983), DOI: 10.1016/0375-9601(83)90764-8. Crossref, Web of Science, ADS, Google Scholar
J. J. C. Nimmo and N. C. Freeman, Phys. Lett. A 95, 4 (1983), DOI: 10.1016/0375-9601(83)90765-X. Crossref, Web of Science, ADS, Google Scholar
J. J. C. Nimmo and N. C. Freeman, Phys. Lett. A 96, 443 (1984), DOI: 10.1016/0375-9601(83)90159-7. Crossref, Web of Science, ADS, Google Scholar
W. X. Ma, Phys. Lett. A 301, 35 (2002), DOI: 10.1016/S0375-9601(02)00971-4. Crossref, Web of Science, ADS, Google Scholar
W. X. Ma and K. I. Maruno, Physica A 343, 219 (2004). Crossref, Web of Science, ADS, Google Scholar
W. X. Ma and Y. C. You, Trans. Amer. Math. Soc. 357, 1753 (2005), DOI: 10.1090/S0002-9947-04-03726-2. Crossref, Web of Science, Google Scholar
C. X. Liet al., Inv. Probl. 23, 279 (2007), DOI: 10.1088/0266-5611/23/1/015. Crossref, Web of Science, ADS, Google Scholar

Journal cover image

Vol. 25, No. 05

Metrics

Downloaded 40 times

History

Received 27 April 2008

Revised 22 May 2008

Keywords