论文标题
具有双功率非线性的1D NLKG方程的多solitons的条件稳定性
Conditional stability of multi-solitons for the 1D NLKG equation with double power nonlinearity
论文作者
论文摘要
我们考虑具有双重功率的一维非线性klein-gordon方程 \ begin {equation*} \ partial_ {t}^{2} u- \ partial_ {x}^{2} u+U+U- | \ end {equation*} $ 1 <q <p <\ infty $。主要结果指出了能量空间中的稳定性$ h^{1}（\ Mathbb {r}）\ times l^{2}（\ Mathbb {r}）$的n n is单单波和不同速度的分支总和。该证明的灵感来自于Martel，Merle和Tsai的类似情况下，针对广义Korteweg-De Vries方程和非线性Schrödinger方程开发的技术的启发[14,15]。但是，该策略对波型方程的适应需要引入适合Lorentz变换的新能量功能。
We consider the one-dimensional nonlinear Klein-Gordon equation with a double power focusing-defocusing nonlinearity \begin{equation*} \partial_{t}^{2}u-\partial_{x}^{2}u+u-|u|^{p-1}u+|u|^{q-1}u=0,\quad \mbox{on}\ [0,\infty)\times \mathbb{R}, \end{equation*} with $1<q<p<\infty$. The main result states the stability in the energy space $H^{1}(\mathbb{R})\times L^{2}(\mathbb{R})$ of the sums of decoupled solitary waves with different speeds, up to the natural instabilities. The proof is inspired by the techniques developed for the generalized Korteweg-de Vries equation and the nonlinear Schrödinger equation in a similar context by Martel, Merle and Tsai [14,15]. However, the adaptation of this strategy to a wave-type equation requires the introduction of a new energy functional adapted to the Lorentz transform.
