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Existence of multi-travelling waves in capillary fluids
Proceedings of the Royal Society of Edinburgh Section A: Mathematics ( IF 1.3 ) Pub Date : 2019-08-19 , DOI: 10.1017/prm.2019.51
Corentin Audiard

We prove the existence of multi-soliton and kink-multi-soliton solutions of the Euler–Korteweg system in dimension one. Such solutions behave asymptotically in time like several travelling waves far away from each other. A kink is a travelling wave with different limits at ±∞. The main assumption is the linear stability of the solitons, and we prove that this assumption is satisfied at least in the transonic limit. The proof relies on a classical approach based on energy estimates and a compactness argument.

中文翻译:

毛细管流体中存在多行波

我们证明了 Euler-Korteweg 系统在第一维的多孤子和扭结多孤子解的存在。这样的解在时间上表现为渐近的,就像几个相距很远的行波。扭结是在 ±∞ 处具有不同限制的行波。主要假设是孤子的线性稳定性,我们证明了这个假设至少在跨音速极限中得到满足。该证明依赖于基于能量估计和紧凑性论证的经典方法。
更新日期:2019-08-19
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