Description of the Inelastic Collision of Two Solitary Waves for the BBM Equation
Description of the Inelastic Collision of Two Solitary Waves for the BBM Equation
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DOI：
10.1007/s00205-009-0244-7
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发表时间：
2008-03
影响因子：
2.5
通讯作者：
Y. Martel;F. Merle;Tetsu Mizumachi
中科院分区：
文献类型：
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作者：
Y. Martel;F. Merle;Tetsu Mizumachi
我们证明了BBM方程的两个孤立波的碰撞是非弹性的，但当其中一个孤立波在能量空间中很小时，几乎是弹性的。我们精确估计的非零残留由于碰撞。此外，我们给出了一个精确的描述的碰撞现象（孤立波的大小和移动轨迹的变化）。为了证明这些结果，我们扩展了Martel和Merle（描述四次gKdV方程的两个孤子碰撞，提交预印本）中介绍的方法。 http://arxiv.org/abs/0709.2672 ; Commun Math Phys 286：39-79，2009），特别是在四次情况下。主要的论点是在碰撞区域的显式近似解的建设。
We prove that the collision of two solitary waves of the BBM equation is inelastic but almost elastic in the case where one solitary wave is small in the energy space. We show precise estimates of the nonzero residue due to the collision. Moreover, we give a precise description of the collision phenomenon (change of size of the solitary waves and shifts in their trajectories). To prove these results, we extend the method introduced in Martel and Merle (Description of two soliton collision for the quartic gKdV equation, submitted preprint. http://arxiv.org/abs/0709.2672 ; Commun Math Phys 286:39–79, 2009) for the generalized KdV equation, in particular in the quartic case. The main argument is the construction of an explicit approximate solution in the collision region.