组合KdV方程孤立波解的轨道稳定性

组合KdV方程在物理学的许多领域都有应用，例如等离子体磁流波、离子声波等。粒子在传输过程中需要刻画其稳定性。本文主要通过平移变换，将研究带有非零渐近值的孤立波解的轨道稳定性，转化为研究具有零渐进值孤立波解的轨道稳定性，给出了稳定性的判定定理，应用Grillakis-Shatah-Strauss提出的轨道稳定性理论与谱分析理论得到了组合KdV方程的几种孤立波解的轨道稳定性结论。

Orbital Stability of Solitary Wave Solutions to the Compound KdV Equations

The compound KdV equation is applied in many fields of physics, such as plasma magnetic current wave, ion acoustic wave and so on. It is necessary to characterize the stability of particles during their propagation. The study of the orbital stability of solitary wave solutions with non-zero asymptotic values is transformed into the study of orbital stability of solitary wave solutions with zero asymptotic values through translation transformation, and the determination theorem of stability is given. The orbital stability theory proposed by Grillakis-Shatah-Strauss and the spectral analysis theory are used to obtain the orbital stability conclusions of the compound KdV equations for several solitary wave solutions.