慢变gKdV方程孤子的非弹性character
Inelastic character of solitons of slowly varying gKdV equations
摘要：
本文讨论了一类慢变gKdV方程孤子的非弹性性质。我们给出了精确的下界，在能量空间中，缺陷引起的潜在的解决方案，随着时间走向无穷大。对于证明，我们认为合适的李雅普诺夫泛函传播的缺陷沿动态在一个非平凡的方式，在精神上的Martel和Merle最近取得的突破的情况下，两个孤子碰撞不可积的gKdV方程。此外，我们还考虑了一个特殊的，退化的情况下，缺陷是正式的二阶。
英文摘要：
In this paper we describe the inelastic character of solitons of some slowly varying gKdV equations. We give precise lower bounds, in the energy space, of the defect induced by the potential on the solution as time goes to infinite. For the proof, we consider suitable Lyapunov functionals that propagate the defect along the dynamics in a non trivial fashion, in the spirit of the recent breakthroughs made by Martel and Merle in the case of the two soliton collision for non integrable gKdV equations. In addition, we also consider a special, degenerate case, where the defect is formally of second order.
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