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An algebraic method exactly solving two high-dimensional nonlinear evolution equations. (English) Zbl 1069.35065

Summary: An algebraic method is applied to construct soliton solutions, doubly periodic solutions and a range of other solutions of physical interest for two high-dimensional nonlinear evolution equations. Among them, the Jacobi elliptic periodic solutions exactly degenerate to the solutions at a certain limit condition. Compared with most existing tanh methods, the proposed method gives new and more general solutions. More importantly, the method provides a guideline to classify the various types of the solutions according to some parameters.

MSC:

35Q51 Soliton equations
37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems

Software:

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References:

[1] Ablowitz, M. J.; Segur, H., Soliton and the inverse scattering transformation (1981), SIAM: SIAM Philadelphia, PA · Zbl 0299.35076
[2] Beals, R.; Coifman, R. R., Comm. Pure. Appl. Math., 37, 39-90 (1984)
[3] Matveev, V. B.; Salle, M. A., Darboux transformation and solitons (1991), Springer: Springer Berlin · Zbl 0744.35045
[4] Gu, C. H.; Hu, H. S.; Zhou, Z. X., Darboux transformations in soliton theory and its geometric applications (1999), Shanghai Sci. Tech. Publ
[5] Leble, S. B.; Ustinov, N. V., J. Phys. A, 26, 5007-5016 (1993)
[6] Esteevez, P. G., J. Math. Phys., 40, 1406-1419 (1999)
[7] Dubrousky, V. G.; Konopelchenko, B. G., J. Phys. A, 27, 4719-4721 (1994)
[8] Neugebauer, G.; Kramerl, D., J. Phys. A, 16, 1927-1936 (1983)
[9] Fan, E. G., J. Math. Phys., 42, 4327-4344 (2001)
[10] Fan, E. G., J. Phys. A, 33, 6925-6933 (2000)
[11] Hirota, R.; Satsuma, J., Phys. Lett. A, 85, 407-408 (1981)
[12] Satsuma, J.; Hirota, R., J. Phys. Soc. Jpn., 51, 3390-3397 (1982)
[13] Tam, H. W.; Ma, W. X.; Hu, X. B.; Wang, D. L., J. Phys. Soc. Jpn., 69, 45-51 (2000)
[14] Malfliet, W., Am.J. Phys., 60, 650-654 (1992)
[15] Hereman, W., Comp. Phys. Comm., 65, 143 (1996)
[16] Malfliet, W.; Hereman, W., Phys. Scripta., 56, 563 (1996)
[17] Parkes, E. J., J. Phys. A, 27, L497 (1994)
[18] Parkes, E. J.; Duffy, B. R., Comput. Phys. Commun., 98, 288 (1996)
[19] Fan, E. G., Phys. Lett. A, 277, 212-218 (2000)
[20] Fan, E. G., J. Phys. A, 36, 7009 (2003) · Zbl 1167.35324
[21] Fan, E. G.; Hon, Y. C., Chaos, Solitons & Fractals, 15, 559-566 (2003)
[22] Wang, L. Y.; Lou, S. Y., Commun. Theor. Phys., 33, 683 (2000)
[23] Senthilvelan, M., Appl. Math. Comput., 123, 386 (2001)
[24] Lou, S. Y., J. Phys. A, 29, 5989 (1996) · Zbl 0903.35064
[25] Hong, W. Y.; Oh, K. S., Comput. Math. Appl., 39, 29 (2000)
[26] Zhang, J. F.; Wu, F. M., Chinese Phys., 11, 425 (2002)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.