Nonlinear polarization waves in a two-component Bose-Einstein condensate

A two-component Bose-Einstein condensate whose dynamics is described by a system of coupled Gross-Pitaevskii equations accommodates waves with different symmetries. A first type of waves corresponds to excitations for which the motion of both components is locally in phase. For the second type of waves, the two components have a counterphase local motion. When the values of the inter-and intracomponent interaction constants are different, the long-wavelength behavior of these two modes corresponds to two types of sound with different velocities. In the limit of weak nonlinearity and small dispersion, the first mode is described by the well-known Korteweg-de Vries equation. In the same limit, we show that the second mode can be described by the Gardner equation if the values of the two intracomponent interaction constants are sufficiently close. This leads to a rich variety of nonlinear excitations (solitons, kinks, algebraic solitons, breathers) which do not exist in the Korteweg-de Vries description.