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Conditional stability of multi-solitons for the 1D NLKG equation with double power nonlinearity
Annales de l'Institut Henri Poincaré C, Analyse non linéaire ( IF 1.8 ) Pub Date : 2020-12-01 , DOI: 10.1016/j.anihpc.2020.11.008
Xu Yuan 1
Affiliation  

We consider the one-dimensional nonlinear Klein-Gordon equation with a double power focusing-defocusing nonlinearityt2ux2u+u|u|p1u+|u|q1u=0,on[0,)×R, where 1<q<p<. The main result states the stability in the energy space H1(R)×L2(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.



中文翻译:

具有双幂非线性的一维NLKG方程多孤子的条件稳定性

我们考虑具有双倍聚焦-散焦非线性的一维非线性 Klein-Gordon 方程2-X2+-||-1+||q-1=0,[0,)×电阻, 在哪里 1<q<<. 主要结果表明能量空间的稳定性H1(电阻)×2(电阻)具有不同速度的去耦孤立波的总和,直到自然不稳定性。该证明的灵感来自于 Martel、Merle 和 Tsai [14]、[15] 在类似上下文中为广义 Korteweg-de Vries 方程和非线性薛定谔方程开发的技术。然而,这种策略对波型方程的适应需要引入适应洛伦兹变换的新能量函数。

更新日期:2020-12-01
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