论文标题
BousSinesQ类型系统中的行驶波
Travelling waves in the Boussinesq type systems
论文作者
论文摘要
本文考虑的是Boussinesq类型系统建模地表水波的许多变体。这种方程是由不同的作者得出的，以描述长重力波的双向传播。特殊解决方案的存在问题，即所谓的孤立波，是一个特别的兴趣。有许多研究依赖于变分方法和浓度 - 紧凑性论点。这些证据在技术上非常苛刻，并且可能因一个系统而异。我们的方法基于隐式函数定理，这使得处理更加容易，更统一。
Considered herein are a number of variants of the Boussinesq type systems modeling surface water waves. Such equations were derived by different authors to describe the two-way propagation of long gravity waves. A question of existence of special solutions, the so called solitary waves, is of a particular interest. There are a number of studies relying on a variational approach and a concentration-compactness argument. These proofs are technically very demanding and may vary significantly from one system to another. Our approach is based on the implicit function theorem, which makes the treatment easier and more unified.
