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标题：Periodic and Solitary-Wave Solutions for a Variant of the <svg style="vertical-align:-3.186pt;width:63.887501px;" id="M1" height="19.25" version="1.1" viewBox="0 0 63.887501 19.25" width="63.887501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.25)"> <g transform="translate(72,-56.6)"> <text transform="matrix(1,0,0,-1,-71.95,59.83)"> <tspan style="font-size: 17.93px; " x="0" y="0">𝐾</tspan> <tspan style="font-size: 17.93px; " x="13.664946" y="0">(</tspan> <tspan style="font-size: 17.93px; " x="19.636635" y="0">3</tspan> <tspan style="font-size: 17.93px; " x="28.603134" y="0">,</tspan> <tspan style="font-size: 17.93px; " x="36.063263" y="0">2</tspan> <tspan style="font-size: 17.93px; " x="45.029762" y="0">)</tspan> </text> </g> </g> </svg> Equation
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作者：Jiangbo Zhou ; Lixin Tian
期刊名称：International Journal of Differential Equations
印刷版ISSN：1687-9643
电子版ISSN：1687-9651
出版年度：2011
卷号：2011
DOI：10.1155/2011/582512
出版社：Hindawi Publishing Corporation
摘要：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.