  It is well known that the nonlinear Schr\"odinger (NLS) equation is a very
important integrable equation. Ablowitz and Musslimani introduced and
investigated an integrable nonlocal NLS equation through inverse scattering
transform. Very recently, we proposed an integrable nonlocal modified
Korteweg-de Vries equation (mKdV) which can also be found in a paper of
Ablowitz and Musslimani. We have constructed the Darboux transformation and
soliton solutions for the nonlocal mKdV equation. In this paper, we will
investigate further the nonlocal mKdV equation. We will give its exact
solutions including soliton and breather through inverse scattering
transformation. These solutions have some new properties, which are different
from the ones of the mKdV equation.

Exactly Solvable and Integrable Systems