New Homoclinic and Heteroclinic Solutions for Zakharov System

A new type of homoclinic and heteroclinic solutions, i.e. homoclinic and heteroclinic breather solutions, for Zakharov system are obtained using extended homoclinic test and two-soliton methods, respectively. Moreover, the homoclinic and heteroclinic structure with local oscillation and mechanical feature different from homoclinic and heterocliunic solutions are investigated. Result shows complexity of dynamics for complex nonlinear evolution system. Moreover, the similarities and differences between homoclinic (heteroclinic) breather and homoclinic (heteroclinic) tube are exhibited. These results show that the diversity of the structures of homoclinic and heteroclinic solutions.