Abstract
We discuss the Darboux transformation method for a modified Korteweg–de Vries equation with variable coefficients and perturbing terms in detail based on the general form of the Darboux transformations for some nonlinear evolution equations solvable by the Ablowitz–Kaup–Newell–Segur inverse scattering method. We use this method to generate families of two-soliton solutions and two-periodic solutions.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
R. Hirota, J. Phys. Soc. Japan, 33, 1456–1458 (1972).
Y. Huang, Nonlinear Dynam., 77, 437–444 (2014).
Y. S. Kivshar and B. A. Malomed, Rev. Modern Phys., 61, 763–915 (1989).
J. Mason and E. Knobloch, Phys. D, 205, 100–124 (2005).
J. L. Hu, X. Feng, and Z. Li, Commun. Nonlinear Sci. Numer. Simul., 5, 118–124 (2000).
H. Triki and A.-M. Wazwaz, Commun. Nonlinear Sci. Numer. Simul., 19, 404–408 (2014).
H. Liu, J. Li, and L. Liu, J. Math. Anal. Appl., 368, 551–558 (2010).
A. H. Khater, M. M. Hassan, and R. S. Temsah, Math. Comput. Simul., 70, 221–226 (2005).
S. Bilige and T. Chaolu, Appl. Math. Comput., 216, 3146–3153 (2010).
A.-M. Wazwaz, Commun. Nonlinear Sci. Numer. Simul., 12, 904–909 (2007).
A.-M. Wazwaz, Commun. Nonlinear Sci. Numer. Simul., 12, 1172–1180 (2007).
A.-M. Wazwaz, Commun. Nonlinear Sci. Numer. Simul., 15, 3270–3273 (2010).
Y. Zarmi, Phys. D, 237, 2987–3007 (2008).
A. Veksler and Y. Zarmi, Phys. D, 217, 77–87 (2006); arXiv:nlin/0505042v1 (2005).
X. Jiao and H.-Q. Zhang, Appl. Math. Comput., 172, 664–677 (2006).
J. Yu, W. Zhang, and X. Gao, Chaos Solitons Fractals, 33, 1307–1313 (2007).
X. Jiao, Y. Zheng, and B. Wu, Appl. Math. Comput., 218, 8486–8491 (2012).
C. Gu, H. Hu, and Z. Zhou, “Darboux transformation,” in: Soliton Theory and Its Applications On Geometry, Shanghai Scientific and Technical Publishers, Shanghai (2005), pp. 5–46.
Author information
Authors and Affiliations
Corresponding author
Additional information
Prepared from an English manuscript submitted by the authors; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 184, No. 2, pp. 244–252, August, 2015.
Rights and permissions
About this article
Cite this article
Huang, Y., Liang, L. Exact two-soliton solutions and two-periodic solutions of the perturbed mKdV equation with variable coefficients. Theor Math Phys 184, 1106–1113 (2015). https://doi.org/10.1007/s11232-015-0320-0
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11232-015-0320-0