Coupled Gerdjikov-Ivanov System and its Exact Solutions through Darboux Transformation

Abstract

The coupled Gerdjikov-Ivanov (GI) system is discussed and its elementary Darboux transformation (DT) is constructed. From elementary (DT), we constructed 2N-fold (DT). The symmetrical properties of the Lax pair and iteration of 2N-fold (DT) give different types of solutions for both zero seed and non-zero seed. Zero seed solutions include brightbright (one and two) Soliton solutions. In non-zero seed solutions, we obtained breather, Ma breather, dark-bright Soliton, breather fission, and dark-bright rogue wave solutions are obtained and plot it.