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Symbolic computation and new families of exact solutions to the \((2 + 1)\)-dimensional dispersive long-wave equations. (English) Zbl 1142.35360

Summary: We present a further generalized algebraic method to the \((2 + 1)\)-dimensional dispersive long-wave equations (DLWS), As a result, we can obtain abundant new formal exact solutions of the equation. The method can also be applied to solve more \((2 + 1)\)-dimensional (or \((3 + 1)\)-dimensional) nonlinear partial differential equations (NPDEs).

MSC:

35C10 Series solutions to PDEs
35-04 Software, source code, etc. for problems pertaining to partial differential equations
35G20 Nonlinear higher-order PDEs

Software:

Maple; PDEtools
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Full Text: DOI

References:

[1] Ablowitz, M. J.; Clarkson, P. A., Soliton, nonlinear evolution equations and inverse scatting (1991), Cambridge University Press: Cambridge University Press New York · Zbl 0762.35001
[2] Wadati, M.; Sanuki, H.; Konno, K., Prog Theoret Phys, 17, 1652 (1975)
[3] Li, B.; Chen, Y.; Zhang, H. Q., Phys Lett A, 305, 377 (2002)
[4] Tam, H. W.; Ma, W. X.; Hu, X. B.; Wang, D. L., J Phys Soc Jpn, 69, 45 (2000)
[5] Wang, M. L.; Wang, Y. M.; Zhou, Y. B., Phys Lett A, 203, 45 (2002)
[6] Fan, E., Phys Lett A, 285, 373 (2001)
[7] Yan, Z. Y.; Zhang, H. Q., Appl Math Mech, 21, 382 (2000)
[8] Chen, Y.; Li, B., Chaos, Solitons & Fractals, 19, 977 (2004)
[9] Fan, E., Phys Lett A, 19, 1141 (2004)
[10] Chandrasekharan, K., Elliptic function (1978), Springer: Springer Berlin
[11] Patrick, D. V., Elliptic function and elliptic curves (1973), Cambridge University Press: Cambridge University Press Cambridge
[12] Wang, Z. X.; Xia, X. J., Special functions (1989), World Scientific: World Scientific Singapore
[13] Boiti, P.; Leon, J. J.P.; Manna, M.; Pempinelli, F., Inverse Probl, 3, 371 (1987)
[14] Paquin, G.; Winternitz, P., Physica D, 46, 122 (1990)
[15] Lou, S. Y., Math Meth Appl Sci, 18, 789 (1995)
[16] Chen, Y.; Wang, Q.; Li, B., Chaos, Solitons & Fractals, 22, 675 (2004)
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.