Geodesic
Exact two-soliton solutions and two-periodic solutions for the perturbed mKdV equation with variable coefficients
Teoretičeskaâ i matematičeskaâ fizika, Tome 184 (2015) no. 2, pp. 244-252 Cet article a éte moissonné depuis la source Math-Net.Ru

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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.
Mots-clés : Darboux transformation
Keywords: perturbed mKdV equation, two-soliton solution, two-periodic solution. 
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     title = {Exact two-soliton solutions and two-periodic solutions for the perturbed {mKdV} equation with variable coefficients},
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Ying Huang; Lin Liang. Exact two-soliton solutions and two-periodic solutions for the perturbed mKdV equation with variable coefficients. Teoretičeskaâ i matematičeskaâ fizika, Tome 184 (2015) no. 2, pp. 244-252. http://geodesic.mathdoc.fr/item/TMF_2015_184_2_a3/

[1] R. Hirota, J. Phys. Soc. Japan, 33:5 (1972), 1456–1458 | DOI | MR

[2] Y. Huang, Nonlinear Dynam., 77:3 (2014), 437–444 | DOI | MR | Zbl

[3] Y. S. Kivshar, B. A. Malomed, Rev. Modern Phys., 61:4 (1989), 763–915 | DOI

[4] J. Mason, E. Knobloch, Phys. D, 205:1–4 (2005), 100–124 | DOI | MR | Zbl

[5] J. L. Hu, X. Feng, Z. Li, Commun. Nonlinear Sci. Numer. Simul., 5:3 (2000), 118–124 | DOI | MR | Zbl

[6] H. Triki, A.-M. Wazwaz, Commun. Nonlinear Sci. Numer. Simul., 19:3 (2014), 404–408 | DOI | MR

[7] H. Liu, J. Li, L. Liu, J. Math. Anal. Appl., 368:2 (2010), 551–558 | DOI | MR | Zbl

[8] A. H. Khater, M. M. Hassan, R. S. Temsah, Math. Comput. Simul., 70:4 (2005), 221–226 | DOI | MR | Zbl

[9] S. Bilige, T. Chaolu, Appl. Math. Comput., 216:11 (2010), 3146–3153 | DOI | MR | Zbl

[10] A.-M. Wazwaz, Commun. Nonlinear Sci. Numer. Simul., 12:6 (2007), 904–909 | DOI | MR | Zbl

[11] A.-M. Wazwaz, Commun. Nonlinear Sci. Numer. Simul., 12:7 (2007), 1172–1180 | DOI | MR | Zbl

[12] A.-M. Wazwaz, Commun. Nonlinear Sci. Numer. Simul., 15:11 (2010), 3270–3273 | DOI | MR | Zbl

[13] Y. Zarmi, Phys. D, 237:23 (2008), 2987–3007 | DOI | MR | Zbl

[14] A. Veksler, Y. Zarmi, Phys. D, 217:1 (2006), 77–87, arXiv: nlin/0505042 | DOI | MR | Zbl

[15] X. Jiao, H.-Q. Zhang, Appl. Math. Comput., 172:1 (2006), 664–677 | DOI | MR | Zbl

[16] J. Yu, W. Zhang, X. Gao, Chaos Solitons Fractals, 33:4 (2007), 1307–1313 | DOI | MR | Zbl

[17] X. Jiao, Y. Zheng, B. Wu, Appl. Math. Comput., 218:17 (2012), 8486–8491 | DOI | MR | Zbl

[18] C. Gu, H. Hu, Z. Zhou, “Darboux transformation”, Soliton Theory and its Applications On Geometry, Shanghai Scientific and Technical Publishers, Shanghai, 2005, 5–46