Solitary waves in Boussinesq type systems

In the talk I will consider Boussinesq type systems modelling 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. We implement another approach based on the implicit function theorem, which makes the treatment easier and more unified.