## International Journal of Differential Equations

### Periodic and Solitary-Wave Solutions for a Variant of the $K(3,2)$ Equation

#### Abstract

We employ the bifurcation method of planar dynamical systems and qualitative theory of polynomial differential systems to derive new bounded traveling-wave solutions for a variant of the $K(3,2)$ equation. For the focusing branch, we obtain hump-shaped and valley-shaped solitary-wave solutions and some periodic solutions. For the defocusing branch, the nonexistence of solitary traveling wave solutions is shown. Meanwhile, some periodic solutions are also obtained. The results presented in this paper supplement the previous results.

#### Article information

Source
Int. J. Differ. Equ., Volume 2011 (2011), Article ID 582512, 16 pages.

Dates
Accepted: 16 August 2011
First available in Project Euclid: 25 January 2017

https://projecteuclid.org/euclid.ijde/1485313249

Digital Object Identifier
doi:10.1155/2011/582512

Mathematical Reviews number (MathSciNet)
MR2847598

Zentralblatt MATH identifier
1239.34037

#### Citation

Zhou, Jiangbo; Tian, Lixin. Periodic and Solitary-Wave Solutions for a Variant of the $K(3,2)$ Equation. Int. J. Differ. Equ. 2011 (2011), Article ID 582512, 16 pages. doi:10.1155/2011/582512. https://projecteuclid.org/euclid.ijde/1485313249

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