  We consider self-similar solutions to mean curvature evolution of entire
Lagrangian graphs. When the Hessian of the potential function $u$ has
eigenvalues strictly uniformly between -1 and 1, we show that on the potential
level all the shrinking solitons are quadratic polynomials while the expanding
solitons are in one-to-one correspondence to functions of homogenous of degree
2 with the Hessian bound. We also show that if the initial potential function
is cone-like at infinity then the scaled flow converges to an expanding soliton
as time goes to infinity.
