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中文摘要：
应用 Grillakis-Shatah-Strauss 提出的轨道稳定性理论，研究了具有两个非线性项的广义Boussinesq 方程孤波解的轨道稳定性与不稳定性，得到了判断该方程孤波解轨道稳定性的一般性结论。进一步根据方程的两个精确钟状孤波解，推出了它们的轨道稳定判别式的显式表达式，从而具体给出了使这两个孤波解轨道稳定的波速变化区间。另外，分析了方程中两个非线性项作用的大小对这两个孤波解轨道稳定波速变化区间的影响，给出了使这两个孤波解轨道稳定的最大波速变化范围。
英文摘要：
The abstract results of Grillakis-Shatah-Strauss were used directly and the orbital stability and instability of solitary waves solutions for the generalized Boussinesq equations with two nonlinear terms were investigated.The general conclusions on the orbital stability of solitary waves were obtained.Furthermore,the explicit expression of discrimination d″（c ）was deduced according to two exact solitary waves solutions of the equations.And the wave speed interval which makes the two solitary waves stable was given.Moreover,the influence of the interaction between the two nonlinear terms of the equations on the wave speed interval which makes the two solitary waves stable was also analyzed.Finally,the biggest wave speed interval which makes the two solitary waves stable was presented.
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