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Explicit and exact traveling wave solutions of Whitham-Broer-Kaup shallow water equations. (English) Zbl 0969.76517
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.

76B15Water waves, gravity waves; dispersion and scattering, nonlinear interaction
35L05Wave equation (hyperbolic PDE)
35L60Nonlinear first-order hyperbolic equations
Full Text: DOI
[1] Whitham, G. B.: Proc. R. Soc. A. 299, 6 (1967)
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[3] Kaup, D. J.: Prog. theor. Phys.. 54, No. 2, 396 (1975)
[4] Kupershmidt, B. A.: Commun. math. Phys.. 99, No. 1, 51 (1985)
[5] Ablowitz, M. J.: Soliton, nonlinear evolution equations and inverse scatting. (1991)
[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, No. 8, 667 (1998)
[9] Wu, W. T.: Polynomial equation-solving and its application, algorithms and computation. (1994)