×

zbMATH — the first resource for mathematics

Exact travelling wave solutions of the Whitham-Broer-Kaup and Broer-Kaup-Kupershmidt equations. (English) Zbl 1069.35067
Summary: It is found that the auxiliary equation method is also applicable to a coupled system of two different equations involving both even-order and odd-order partial derivative terms. Furthermore, singular travelling wave solutions can also be obtained by considering other types of exact solutions of auxiliary equation. The Whitham-Broer-Kaup and the (2 + 1)-dimensional Broer-Kaup-Kupershmidt equations are chosen as examples to illustrate the effectiveness of the auxiliary equation method.

MSC:
35Q51 Soliton equations
37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems
Software:
MACSYMA; RATH
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Ablowitz, M.J.; Clarkson, P.A., Solitons, nonlinear evolution equations and inverse scattering, (1991), Cambridge University Press Cambridge · Zbl 0762.35001
[2] Wadati, M.; Sanuki, H.; Konno, K., Prog. theor. phys., 53, 419, (1975)
[3] Konno, K.; Wadati, M., Prog. theor. phys., 53, 1652, (1975)
[4] Gu, C.H., Soliton theory and its application, (1995), Springer Berlin
[5] Hirota, R., Phys. rev. lett., 27, 1192, (1971)
[6] Hereman, W.; Takaoka, M., J. phys. A: math. gen., 23, 4805, (1990) · Zbl 0719.35085
[7] Xu, G.Q.; Li, Z.B., Acta phys. sin., 51, 1424, (2002), [in Chinese]
[8] Malfliet, W., Am. J. phys., 60, 650, (1992)
[9] Fan, E.G., Phys. lett. A, 277, 212, (2000)
[10] Yao, R.X.; Li, Z.B., Phys. lett. A, 297, 196, (2002)
[11] Liu, Y.P.; Li, Z.B., Comp. phys. commun., 155, 65, (2002)
[12] Li, Z.B.; Wang, M.L., J. phys. A: math. gen., 26, 6027, (1993)
[13] Wang, M.L., Phys. lett. A, 199, 169, (1995)
[14] Yan, C., Phys. lett. A, 224, 77, (1996)
[15] Feng, X., Phys. lett. A, 213, 167, (1996)
[16] Feng, X., Inter. J. theor. phys., 39, 207, (2000)
[17] Liu, S.K.; Fu, Z.T.; Liu, S.D.; Zhao, Q., Phys. lett. A, 289, 69, (2001)
[18] Fu, Z.T.; Liu, S.K.; Liu, S.D.; Zhao, Q., Phys. lett. A, 290, 72, (2001)
[19] Sirendaoreji; Jiong, S., Phys. lett. A, 309, 387, (2003)
[20] Sirendaoreji, Chaos, solitons & fractals, 19, 147, (2004)
[21] Kupershmidt, B.A., Commun. math. phys., 99, 51, (1985)
[22] Yan, Z.Y.; Zhang, H.Q., Phys. lett. A, 285, 355, (2001)
[23] Zakharov, V.E., J. appl. meth. tech. phys. (USSR), 9, 190, (1968)
[24] Ruan, H.Y.; Chen, Y.X., Acta phys. sin. (overseas edition), 7, 241, (1998)
[25] Ying, J.P.; Lou, S.Y., Z. naturforsch. A, 56, 619, (2001)
[26] Li, D.S.; Zhang, H.Q., Chaos, solitons & fractals, 18, 193, (2003)
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.