Generalized perturbed complex Toda chain for Manakov system and exact solutions of Bose–Einstein mixtures

We analyze, both analytically and numerically, the dynamical behavior of the N-soliton train in the Manakov system with perturbations due to an external potential. The perturbed complex Toda chain model has been employed to describe adiabatic interactions within the N Manakov-soliton train. Simulations performed demonstrate that external potentials can play a stabilizing role to provide bound state regime of the train propagation. We also present new stationary and travelling wave solutions to equations describing Bose–Fermi mixtures in an elliptic external potential. Precise conditions for the existence of every class of solutions are derived. There are indications that such waves and localized objects may be observed in experiments with cold quantum degenerate gases.