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On the extended applications of homogeneous balance method. (English) Zbl 1032.35159

Summary: We study the travelling wave reductions for certain \((2+1)\)- and \((3+1)\)-dimensional physically important nonlinear evolutionary equations by using the recently proposed homogeneous balance method (HBM). Through this analysis we explore certain new solutions.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
35Q58 Other completely integrable PDE (MSC2000)
35C05 Solutions to PDEs in closed form
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[1] Ablowitz, M. J.; Clarkson, P. A., Solitons, Nonlinear Evolution Equations and Inverse Scattering Transform (1990), Cambridge University Press: Cambridge University Press Cambridge · Zbl 0762.35001
[2] Konopelchenko, B. G., Solitons in Multidimensions (1993), World Scientific Press: World Scientific Press Singapore · Zbl 0836.35002
[3] Lakshmanan, M.; Radha, R., Pramana-J. Phys., 48, 163 (1997), (and references therein)
[4] Paquin, G.; Winternitz, P., Physica D, 46, 122 (1990), (and references therein)
[5] Faucher, M.; Winternitz, P., Phys. Rev. E, 48, 3066 (1993)
[6] Senthil Velan, M.; Lakshmanan, M., J. Nonlinear Math. Phys., 5, 190 (1998) · Zbl 1119.37324
[7] Yan, Z.; Zhang, H., Phys. Lett. A, 252, 291 (1999)
[8] Tian Gao, Y.; Tian, B., Chaos, Solitons and Fractals, 8, 897 (1997)
[9] Tian, B.; Tian Gao, Y., Comput. Phys. Commun., 95, 139 (1996)
[10] Wang, M. L., Phys. Lett. A, 199, 169 (1995)
[11] Wang, M. L., Phys. Lett. A, 213, 279 (1996)
[12] Wang, M. L.; Zhou, Y. B.; Li, Z. B., Phys. Lett. A, 216, 67 (1996)
[13] Fan, E.; Zhang, H., Phys. Lett. A, 245, 389 (1998)
[14] Fan, E.; Zhang, H., Phys. Lett. A, 246, 403 (1998)
[15] Allen, M. A.; Rowlands, G., Phys. Lett. A, 235, 145 (1997)
[16] Dorrizi, B.; Grammaticos, B.; Ramani, A.; Winternitz, P., J. Math. Phys., 27, 2848 (1986)
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.