Focusing mKdV Breather Solutions with Nonvanishing Boundary Conditions by the Inverse Scattering Method

Using the Inverse Scattering Method with a nonvanishing boundary condition, we obtain the square k^2 of a focusing modified Korteweg-de Vries (mKdV) breather solution with non zero vacuum parameter b^2 . We are able to factorize and simplify it in order to get explicitly the associated mKdV breather solution k with non zero vacuum parameter b. Moreover, taking the limiting case of zero frequency, we obtain a generalization of the Double Pole solution introduced by M.Wadati et al.