Unbounded Solutions of the Modified Korteweg-de Vries Equation

In this dissertation we prove local existence and uniqueness of solutions of the focusing modified Korteweg - de Vries equation ut + u2ux + uxxx = 0 in classes of unbounded functions that admit an asymptotic expansion at infinity in decreasing powers of x.

We show that an asymptotic solution differs from a genuine solution by a smooth function that is of Schwartz class with respect to x and that solves a generalized version of the focusing mKdV equation.

The latter equation is solved by discretization methods.