Controlled Fission and Superposition of Vector Solitons in an Integrable Model of Two-Component Bose-Einstein Condensates

Abstract: We investigate the dynamics of vector solitons in a two-component Bose-Einstein condensates governed by the system of Gross-Pitaevskii equations. Using a gauge-transformation approach, we construct a four-soliton solution and analyze their interactions, including superposition states, fission, and shape-preserving collisions. We explore the ability of time-dependent parameters, such as the intra- and intercomponent interaction coefficients and trapping potential, to control the soliton properties. In particular, we demonstrate controlled four-soliton fission, highlighting its potential applications to quantum data processing and coherent matter-wave transport. The results suggest experimental realization in BEC systems and provide insights into nonlinear wave interactions in multicomponent quantum fluids.