论文标题
非线性klein-gordon方程中孤立波的稳定性
Stability of solitary waves in nonlinear Klein-Gordon equations
论文作者
论文摘要
重新审视了一维非线性klein-gordon系统中拓扑孤立波和脉冲的稳定性。 The linearized equation describing small deviations around the static solution leads to a Sturm-Liouville problem, which is solved in a systematic way for the $-l\,(l+1)\,\sech^2(x)$-potential, showing the orthogonality and completeness relations fulfilled by the set of its solutions for all values $l\in\mathbb{N}$.这种方法允许确定某些非线性klein-gordon方程的扭结和脉冲的线性稳定性。引入了两个新型非线性klein-gordon电位的家族。即使未明确知道非线性电势，这些电势的确切溶液（扭结和脉冲）也是精确计算的。发现新型模型的纠结是稳定的，而脉冲不稳定。脉冲的稳定性是通过引入某些空间不均匀性来实现的。
The stability of topological solitary waves and pulses in one-dimensional nonlinear Klein-Gordon systems is revisited. The linearized equation describing small deviations around the static solution leads to a Sturm-Liouville problem, which is solved in a systematic way for the $-l\,(l+1)\,\sech^2(x)$-potential, showing the orthogonality and completeness relations fulfilled by the set of its solutions for all values $l\in\mathbb{N}$. This approach allows to determine the linear stability of kinks and pulses of certain nonlinear Klein-Gordon equations. Two families of novel nonlinear Klein-Gordon potentials are introduced. The exact solutions (kinks and pulses) for these potentials are exactly calculated, even when the nonlinear potential is not explicitly known. The kinks of the novel models are found to be stable, whereas the pulses are unstable. The stability of the pulses is achieved by introducing certain spatial inhomogeneities.
