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摘要: 利用动力系统分支理论和定性理论研究了$K(n,-n,2n)$方程的行波解及其动力学性质. 结合可积系统的特点, 得到系统的孤立行波解,不可数无穷多光滑周期行波解和不光滑行波解;并根据行波解与相轨线间关系,揭示了不同类型行波解间转变与参数变化的关系.Abstract: The traveling wave solutions and the dynamical propertiesof Equation $K(n,-n,2n)$ were studied in terms of the bifurcationtheory of dynamic systems and of the qualitative theory. Based onthe characters of an integrable system, the solitary traveling wavesolutions, uncountably infinite many smooth periodic wave solutionsand non-smooth periodic traveling wave solutions of the system wereobtained. According to the relationship between traveling waves andphase orbits, that changes of parameters led to the transitions oftraveling wave solutions of different types were revealed.
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