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The exact solutions to the complex KdV equation. (English) Zbl 1209.35123
Summary: Wronskian solutions for the complex KdV equation are obtained by Hirota’s bilinear method. Moreover, starting from the bilinear Bäcklund transformation, multi-soliton solutions are presented for the same equation. At the same time, it is also shown that these two kinds of solutions are equivalent.

##### MSC:
 35Q53 KdV equations (Korteweg-de Vries equations) 35A30 Geometric theory, characteristics, transformations in context of PDEs 35Q51 Soliton equations
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##### References:
 [1] Garder, C.S.; Green, J.M.; Miura, M.D., Phys. rev. lett., 19, 1095, (1967) [2] Wadati, M.; Konno, K.; Ichikawa, Y.H., J. phys. soc. jpn., 46, 1965, (1979) [3] Hu, X.B., J. math. phys., 35, 4379, (1994) [4] Wadati, M.; Sanuki, H.; Konno, K., Prog. theor. phys., 53, 419, (1975) [5] Matveev, V.B.; Salle, M.A., Darboux transformations and solitons, (1991), Springer-Verlag Berlin · Zbl 0744.35045 [6] Freeman, N.C.; Nimmo, J.J.C., Phys. lett. A, 95, 1, (1983) [7] Nimmo, J.J.C.; Freeman, N.C., Phys. lett. A, 95, 4, (1983) [8] Nimmo, J.J.C., Phys. lett. A, 99, 281, (1983) [9] Hirota, R., Phys. rev. lett., 27, 1192, (1971) [10] Hirota, R., Direct methods in soliton theory, (), 157 [11] Ablowitz, M.J.; Segur, H., Soliton and the inverse scattering transform, (1981), SIAM Philadelphia · Zbl 0299.35076 [12] Nimmo, J.J.C., Phys. lett. A, 94, 281, (1983) [13] Ma, W.X., Chaos solitons fractals, 19, 163, (2004) [14] Zhang, Y.; Deng, S.F.; Zhang, D.J.; Chen, D.Y., Physics A, 339, 228, (2004) [15] Kerszberg, M., Phys. lett. A, 95, 241, (1984) [16] Levi, D.; Sanielevici, M., Physica D, 98, 510, (1996) [17] Kruskal, M.D., Lect. appl. math., 15, 61, (1974) [18] Yang, L.; Yang, K.Q.; Luo, H.G., Phys. lett. A, 267, 331, (2000) [19] Birnir, B., Commun. pure appl. math., 39, 283, (1986) [20] Oevel, W., Phys. lett. A, 94, 404, (1983) [21] Ma, W.X., J. phys. A, 31, 7585, (1998) · Zbl 0931.35152 [22] Roy, P.K., Phys. lett. A, 249, 55, (1998) [23] Hu, H.C.; Tong, B.; Lou, S.Y., Phys. lett. A, 351, 403, (2006) [24] Bruecker, K.A., Advances in theoretical physics, vol. 1, (1965), Academic Press New York [25] Satsuma, J., J. phys. soc. jpn., 46, 359, (1976) [26] Ma, W.X.; Zhou, D.T., Acta math. sci., 17, 168, (1997) [27] Ma, W.X., Phys. lett. A, 301, 35, (2002) [28] Ma, W.X.; You, Y.C., Trans. am. math. soc., 357, 1753, (2005)
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