Xie, F.; Yan, Z.; Zhang, H. Explicit and exact traveling wave solutions of Whitham-Broer-Kaup shallow water equations. (English) Zbl 0969.76517 Phys. Lett., A 285, No. 1-2, 76-80 (2001). Summary: In this Letter, four pairs solutions of Whitham-Broer-Kaup (WBK) equations, which contain blow-up solutions and periodic solutions, are obtained by using of hyperbolic function method, Mathematica and Wu elimination method. The method can also be applied to solve more nonlinear partial differential equation or equations. Cited in 1 ReviewCited in 41 Documents MSC: 76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction 35L05 Wave equation 35L60 First-order nonlinear hyperbolic equations Keywords:hyperbolic function method; Wu elimination method PDFBibTeX XMLCite \textit{F. Xie} et al., Phys. Lett., A 285, No. 1--2, 76--80 (2001; Zbl 0969.76517) Full Text: DOI References: [1] Whitham, G. B., Proc. R. Soc. A, 299, 6 (1967) [2] Broer, L. J., Appl. Sci. Res., 31, 5, 377 (1975) [3] Kaup, D. J., Prog. Theor. Phys., 54, 2, 396 (1975) [4] Kupershmidt, B. A., Commun. Math. Phys., 99, 1, 51 (1985) [5] Ablowitz, M. J., Soliton, Nonlinear Evolution Equations and Inverse Scatting (1991), Cambridge University Press: Cambridge University Press New York [6] Wang, M. L., Phys. Lett. A, 199, 169 (1995) [7] Yan, Z. Y.; Zhang, H. Q., Phys. Lett. A, 252, 291 (1999) [8] Fan, E. G.; Zhang, H. Q., Appl. Math. Mech., 19, 8, 667 (1998), in Chinese [9] Wu, W. T., Polynomial Equation-Solving and Its Application, Algorithms and Computation (1994), Springer: Springer Berlin, p. 1 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.