zbMATH — the first resource for mathematics

Travelling wave solutions to a higher order KdV equation. (English) Zbl 0732.76012
Summary: This paper presents a direct method for the construction of travelling wave solutions to a higher order KdV equation. The method is based on a general form of solution to both the KdV equation and the fifth order KdV equation. In this approach a number of unknown constants are involved, and it is shown that the equations governing them are properly determined. The form of the solution depends on the signs of the coefficients b and c in the higher order KdV equation.

76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
35Q53 KdV equations (Korteweg-de Vries equations)
Full Text: DOI
[1] Yoshimura, K.; Watanabe, S., Chaotic behavior of nonlinear equation with fifth order dispersion, J. phys. Japan, 51, 3025-3035, (1982)
[2] Kano, K.; Nakayama, T., An exact solution of the wave equation: u_{t} + uux − u5x = 0, J. phys. soc. Japan, 50, 361-362, (1981)
[3] Yamamoto, Y.; Takizawa, E., On a solution of a nonlinear time-evolution equation of fifth order, J. phys. soc. Japan, 45, 1421-1422, (1981)
[4] Kakutani, T.; Ono, H., Weakly nonlinear hydromagnetic waves in a cold collision-free plasma, J. phys. soc. Japan, 26, 1305-1318, (1969)
[5] Hasimoto, H., Water waves — their dispersion and steeping, Kagaku, 40, 401-408, (1970), (in Japanese)
[6] Hunter, J.K.; Vanden-Broeck, J.M., Solitary and periodic gravity-capillary waves of finite amplitude, J. fluid mech., 33, 205-219, (1983) · Zbl 0556.76018
[7] Kawahara, T., Oscillatory waves in dispersive media, J. phys. soc. Japan, 33, 260-264, (1972)
[8] Zufiria, J.A., Symmetry breaking in periodic and solitary gravity-capillary waves on water of finite depth, J. fluid mech., 184, 183-206, (1987) · Zbl 0634.76016
[9] Hunter, J.K.; Scheurle, J., Existence of perturbed solitary wave solutions to a model equation for water waves, Physica D, 33, 253-268, (1988) · Zbl 0694.35204
[10] Hereman, W.; Korpel, A.; Banerjee, P.P., A general physical approach to solitary wave construction from linear solutions, Wave motion, 7, 283-289, (1985)
[11] Freeman, N.C., Soliton interaction in two-dimensions, Advances in applied mechanics, 20, 1-37, (1980) · Zbl 0477.35077
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.