Darboux transformation and dark vector soliton solutions for complex mKdV systems

Abstract

A Darboux transformation and general vector dark soliton solutions are constructed for multi-component complex modified Korteweg–de Vries (mKdV) system. Dark soliton solutions exist when nonlinearities are either defocusing or mixed focusing and defocusing. Single-dark–dark–dark and two-dark–dark–dark soliton solutions of three component complex mKdV system are explicitly presented, whose properties and dynamics are illustrated. It is also shown during the interaction between those solitons, energies in different components completely transmit through. Moreover, we perform an asymptotic analysis for the n -dark soliton solutions rigorously. Our results can be applicable to the study of dark solitons in different physical fields.