论文标题
用对称的1D二次klein-gordon方程的孤子动力学
Soliton dynamics for the 1D quadratic Klein-Gordon equation with symmetry
论文作者
论文摘要
我们在不稳定的孤子的局部能量标准中建立条件渐近稳定性，用于在甚至扰动下的一维二维klein-gordon方程。该问题的一个关键特征是线性化操作员周围表现出的正间隙特征值。我们的证明是基于几种病毒类型的估计值，结合了一系列作品[23-26，28]的技术，并明确验证了费米的黄金法则。该方法取决于即使扰动也与线性化运算符的奇数阈值共振正交。
We establish the conditional asymptotic stability in a local energy norm of the unstable soliton for the one-dimensional quadratic Klein-Gordon equation under even perturbations. A key feature of the problem is the positive gap eigenvalue exhibited by the linearized operator around the soliton. Our proof is based on several virial-type estimates, combining techniques from the series of works [23-26, 28], and an explicitly verified Fermi Golden Rule. The approach hinges on the fact that even perturbations are orthogonal to the odd threshold resonance of the linearized operator.
