Soliton, breather and rogue wave solutions of the coupled Gerdjikov-Ivanov equation via Darboux transformation

摘要

The coupled Gerdjikov-Ivanov (cGI) equation, associated with a 3 x 3 matrix Lax pair, is an important integrable system that can be reduced to the third kind of derivative nonlinear Schrodinger equation, i.e., Gerdjikov-Ivanov equation. Based on the symmetric relations of the Lax pair, 2N-fold Darboux transformation for the cGI equation is constructed. As an application of the Darboux transformation, we obtain some exact solutions of the cGI equation, including bright-bright soliton, dark-bright soliton, Ma breather, breather fission, soliton fusion and dark-bright rogue wave.