N-soliton solutions for the three-component Dirac–Manakov system via Riemann–Hilbert approach

Abstract

This investigation delves into the application of the well-established Riemann–Hilbert method for the elucidation of the N-solitons solution of the three-component Dirac–Manakov system. The analytical process is structured in two fundamental steps. Initially, the inverse scattering method is employed to establish a pivotal connection between the solution of the three-component DiracManakov system and the associated Riemann–Hilbert problem. Subsequently, we systematically address the resolution of this pertinent Riemann–Hilbert problem. Through the assignment of specific values to the relevant parameters in our solution, we adeptly generate graphical representations that vividly illustrate the nuanced dynamics inherent in the solution of the three-component DiracManakov system.