### CAS Seminar

# Haidar Mohamad

### (Jacobs University)

## "A nonvariational construction of slow manifolds for the semi-linear Klein-Gordon equation"

** Date: ** |
Wed, April 13, 2016 |

** Time: ** |
14:15 |

** Place: ** |
Research I Seminar Room |

**Abstract:** We extend a fast-slow nonvariational construction, which was already used for a class of singularly perturbed ODEs, to be applied on the semi-linear Klein-Gordon equation.

We construct an approximate system for the slow motion, whose nonlinear part is an asymptotic series in \(\epsilon\) with coefficient functions recursively defined, up to a small remainder with respect to \(\epsilon\). We prove that the solutions of the slow systems shadow solutions of the Klein-Gordon equation at the corresponding order over a finite interval of time.