Bipolar solitons of the focusing nonlinear Schrödinger equation

The focusing nonlinear Schrödinger equation (NLSE) is a universal model for studying solitary waves propagation in nonlinear media. The NLSE is especially important in understanding how solitons on a condensate background (SCB) appear from a small perturbation through modulation instability. We study theoretically the one- and two-soliton solutions of the NLSE in presence of a condensate by using the dressing method. It is found that a class of bipolar elliptically polarized solitons with the choice of specific parameters in the one- and two-soliton solutions. Collisions among these solitons are studied by qualitative analysis and graphical illustration. We also generalize the concept of the quasi-Akhmediev breather to the bipolar solitons and show how it can be used for wave profile compression down to the extremely short duration. Our results extend previous studies in this area of the SCB and play an important role in the theory of freak wave.