EINSTEIN-INFELD-HOFFMAN METHOD AND SOLITON DYNAMICS IN A PARITY NONINVARIANT SYSTEM

We consider the slow motion of a pointlike topological defect (vortex) in the nonlinear Schrodinger equation minimally coupled to a Chern-Si mons gauge field and subject to an external uniform magnetic field. It turns out that a formal expansion of fields in powers of defect veloc ity yields only the trivial static solution. To obtain a nontrivial so lution one has to treat velocities and accelerations as being of the s ame order. We assume that acceleration is a linear form of velocity. T he field equations linearized in velocity uniquely determine the linea r relation. It turns out that the only nontrivial solution is the cycl otron motion of the vortex together with the whole condensate. This so lution is a perturbative approximation to the center of mass motion kn own from the theory of magnetic translations.