Elongation of moving noncommutative solitons

We discuss the characteristic properties of noncommutative solitons moving with constant velocity. As noncommutativity breaks the Lorentz symmetry, the shape of moving solitons is affected not just by the Lorentz contraction along the velocity direction, but also sometimes by additional ‘elongation’ transverse to the velocity direction. We explore this in two examples: noncommutative solitons in a scalar field theory on two spatial dimension and ‘long stick’ shaped noncommutative U(2) magnetic monopoles. However the elongation factors of these two cases are different, and so not universal.