International Journal of Differential Equations
- Int. J. Differ. Equ.
- Volume 2011 (2011), Article ID 582512, 16 pages.
Periodic and Solitary-Wave Solutions for a Variant of the Equation
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 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.
Int. J. Differ. Equ., Volume 2011 (2011), Article ID 582512, 16 pages.
Received: 5 May 2011
Accepted: 16 August 2011
First available in Project Euclid: 25 January 2017
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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