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PDEBellII: a Maple package for finding bilinear forms, bilinear Bäcklund transformations, Lax pairs and conservation laws of the KdV-type equations. (English) Zbl 1344.37003
Summary: Based on the Bell polynomials scheme, this paper presents a Maple computer algebra program PDEBellII which can automatically construct the bilinear forms, bilinear Bäcklund transformations, Lax pairs and conservation laws of the KdV-type soliton equations. Some examples are given to verify the validity of our program.

MSC:
37-04 Software, source code, etc. for problems pertaining to dynamical systems and ergodic theory
35Q53 KdV equations (Korteweg-de Vries equations)
37K35 Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems
37K05 Hamiltonian structures, symmetries, variational principles, conservation laws (MSC2010)
37K20 Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
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References:
[1] Gilson, C.; Lambert, F.; Nimmo, J.; Willox, R., Proc. R. Soc. Lond. Ser. A, 452, 223, (1996)
[2] Hirota, R., Phys. Rev. Lett., 27, 1192, (1971)
[3] Hirota, R., J. Phys. Soc. Japan, 33, 1456, (1972)
[4] Hirota, R., J. Phys. Soc. Japan, 33, 1459, (1972)
[5] Hirota, R., The direct method in soliton theory, (2004), Cambridge University Press New York
[6] Hietarinta, J., Lecture Notes in Phys., 638, 95, (2004)
[7] Hu, X. B., J. Phys. A: Math. Gen., 26, L465, (1993)
[8] Lambert, F.; Loris, I.; Springael, J.; Willox, R., J. Phys. A: Math. Gen., 27, 8705, (1994)
[9] Lambert, F.; Springael, J., J. Phys. Soc. Japan, 66, 2211, (1997)
[10] Lambert, F.; Loris, I.; Springael, J., Inverse Probl., 17, 1067, (2001)
[11] Lambert, F.; Springael, J., Acta. Appl. Math., 102, 147, (2008)
[12] Lambert, F.; Leble, S.; Springael, J., Glasg. Math. J., 43A, 53, (2001)
[13] Fan, E. G., Phys. Lett. A, 375, 493, (2011)
[14] Hon, Y. C.; Fan, E. G., IMA J. Appl. Math., 77, 2, 236, (2012)
[15] Fan, E. G.; Chow, K. W., J. Math. Phys., 52, 023504, (2011)
[16] Fan, E. G.; Hon, Y. C., J. Math. Phys., 53, 013503, (2012)
[17] Fan, E. G., Stud. Appl. Math., 127, 284, (2011)
[18] Ma, W. X., J. Phys. Conf. Ser., 411, 012021, (2013)
[19] Fan, E. G., Phys. Lett. A, 277, 212, (2000)
[20] Yan, Z. Y., Comput. Phys. Commun., 148, 30, (2002)
[21] Yan, Z. Y., Comput. Phys. Commun., 152, 1, (2003)
[22] Yan, Z. Y., Comput. Phys. Commun., 153, 145, (2003)
[23] Chen, Y.; Zheng, Y., Int. J. Mod. Phys. C, 14, 5, 601, (2003)
[24] Chen, Y.; Li, B., Chaos Solitons Fractals, 19, 977, (2004)
[25] Chen, Y.; Wang, Q., Appl. Math. Comput., 177, 1, 396, (2006)
[26] Hietarinta, J., J. Math. Phys., 28, 1732, (1987)
[27] Hietarinta, J., J. Math. Phys., 28, 2094, (1987)
[28] Hietarinta, J., J. Math. Phys., 28, 2586, (1987)
[29] Hietarinta, J., J. Math. Phys., 29, 628, (1988)
[30] Hereman, W.; Zhuang, W., Symbolic computation of solitons with macsyma, computational and applied mathematics, II (Dublin, 1991), 287-296, (1992), North-Holland Amsterdam · Zbl 0765.35048
[31] Zhou, Z. J.; Fu, J. Z.; Li, Z. B., Appl. Math. Comput., 183, 872, (2006)
[32] Yang, X. D.; Ruan, H. Y., Commun. Theor. Phys., 52, 801, (2009)
[33] Yang, X. D.; Ruan, H. Y., Appl. Math. Comput., 219, 8018, (2013)
[34] Ye, Y. C.; Wang, L. H.; Chang, Z. W.; He, J. S., Appl. Math. Comput., 218, 2200, (2011)
[35] Yang, Y. Q.; Chen, Y., Chin. Ann. Math. Ser. B, (2013), in press
[36] Wang, M. L.; Zhou, Y. B.; Li, Z. B., Phys. Lett. A, 216, 67, (1996)
[37] Wazwaz, A. M., Phys. Scr., 82, 035009, (2010)
[38] Marchant, T. R., Proc. R. Soc. Lond. Ser. A, 456, 433, (2000)
[39] Hirota, R.; Satsuma, J., J. Phys. Soc. Japan, 40, 611, (1976)
[40] Lü, X.; Geng, T.; Zhang, C.; Zhu, H. W.; Meng, X. H.; Tian, B., Int. J. Mod. Phys. B, 23, 25, 5003, (2009)
[41] Senthilvelan, M., Appl. Math. Comput., 123, 381, (2001)
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