得到了该方程的包络孤立波解和包络正弦波解。
And the envelope solitary wave solutions and envelope sinusoidal wave solutions have been obtained.
等的抽象理论，通过谱分析，证明了该孤立波解是轨道稳定的。
By using the abstract results of M. Grillakis et al and careful spectral analysis, we prove that the stability of the solitary waves is orbital.
用行波方法得到了这些方程的显式精确解，即有理分式型孤立波解。
The exact and explicit solutions of these equations are obtained by using the travelling wave method. These exact solutions are solitary wave solutions of a rational type.
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