Homoclinic solutions for Davey-Stewartson equation

In this paper, we firstly prove the existence of homoclinic solutions for Davey-Stewartson I equation (DSI) with the periodic boundary condition. Then we obtain a set of exact homoclinic solutions by the novel method-Hirota’s method. Moreover, the structure of homoclinic solutions has been investigated. At the same time, we give some numerical simulations which validate these theoretical results.