Elliptic traveling waves of the Olver equation. (English) Zbl 1248.35162

Summary: Nonlinear waves on water are studied. The method recently developed by two of the authors [Commun. Nonlinear Sci. Numer. Simul. 15, No. 10, 2778–2790 (2010; Zbl 1222.35160); Commun. Nonlinear Sci. Numer. Simul. 16, No. 3, 1127–1134 (2011; Zbl 1221.34233); Phys. Lett., A 374, No. 39, 4023–4029 (2010; Zbl 1238.34020)] is applied to the Olver water wave equation. New solutions of this equation are found. These solutions are expressed in terms of the Weierstrass elliptic function.


35Q35 PDEs in connection with fluid mechanics
35C07 Traveling wave solutions
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
34M05 Entire and meromorphic solutions to ordinary differential equations in the complex domain
Full Text: DOI


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