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Kudryashov, Nikolai A.; Soukharev, Mikhail B.; Demina, Maria V.

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

Commun. Nonlinear Sci. Numer. Simul. 17, No. 11, 4104-4114 (2012).
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.

Cited in 9 Documents

MSC:

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

Keywords:

nonlinear water wave; elliptic solution; periodic solution; meromorphic solution; Olver equation; nonlinear ordinary differential equation

Citations:

Zbl 1222.35160; Zbl 1221.34233; Zbl 1238.34020
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\textit{N. A. Kudryashov} et al., Commun. Nonlinear Sci. Numer. Simul. 17, No. 11, 4104--4114 (2012; Zbl 1248.35162)
Full Text: DOI

References:

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