论文标题
恒星图上korteweg-de Vries方程的固定溶液的线性不稳定性
Linear instability of stationary solutions for the Korteweg-de Vries equation on a star graph
论文作者
论文摘要
这项工作的目的是在星形图上建立针对Korteweg-de Vries模型的固定解决方案的线性不稳定性标准，其结构由有限的半侵入边缘的有限集合表示。通过考虑$δ$ -Type在图形vertex处的边界条件，我们表明连续的尾巴和凸起轮廓在平衡的星形图中是线性不稳定的。在我们的稳定性分析中，运算符分析扰动理论和对称操作员的扩展理论的使用是基本的。 本研究中提出的论点具有研究恒星图上其他非线性进化方程的固定波解决方案的不稳定性的前景。
The aim of this work is to establish a linear instability criterium of stationary solutions for the Korteweg-de Vries model on a star graph with a structure represented by a finite collections of semi-infinite edges. By considering a boundary condition of $δ$-type interaction at the graph-vertex, we show that the continuous tail and bump profiles are linearly unstable in a balanced star graph. The use of the analytic perturbation theory of operators and the extension theory of symmetric operators is a piece fundamental in our stability analysis. The arguments presented in this investigation has prospects for the study of the instability of stationary waves solutions of other nonlinear evolution equations on star graphs.
