In this paper, symmetry analysis is extended to study nonlocal differential
equations, in particular two integrable nonlocal equations, the nonlocal
nonlinear Schr\"odinger equation and the nonlocal modified Korteweg--de Vries
equation. Lie point symmetries are obtained based on a general theory and used
to reduce these equations to nonlocal and local ordinary differential equations
separately; namely one symmetry may allow reductions to both nonlocal and local
equations depending on how the invariant variables are chosen. For the nonlocal
modified Korteweg--de Vries equation, analogously to the local situation, all
reduced local equations are integrable. At the end, we also define complex
transformations to connect nonlocal differential equations and
differential-difference equations.Comment: 10 page
