Collisional dynamics of solitons and pattern formation in an integrable cross coupled nonlinear Schrödinger equation with constant background

We investigate the dynamics arising out of the propagation of light pulses with different polarizations through a condensate (referred to as a constant background field) with cross coupling described by a coupled nonlinear Schrodinger equation (NLSE) type equation. We then employ Gauge and Darboux transformation approach to bring out the rich dynamics arising out of the background field and cross coupling. The collisional dynamics of bright solitons is found to be inelastic. The constant background field is found to facilitate the periodic localization of light pulses during propagation. We have also unearthed breathers, bright-bright, bright-dark, and dark-bright solitons of the coupled NLSE. While the amplitude of breathers oscillate with time as predicted, their maximum (or minimum) amplitude is found to remain a constant and the addition of cross coupling only contributes to the rapid fluctuations in its amplitude over a period of time. In addition, the reinforcement of cross coupling in the presence of constant wave field facilitates the interference of light pulses leading to interesting pattern formation among bright-bright, bright-dark, and dark-bright solitons. The highlight of the results is that one obtains various localized excitations like breathers, bright, and dark solitons by simply manipulating the amplitude of the constant wave field.