Context : Young planets embedded in their protoplanetary disk interact gravitationally with it leading to energy and angular momentum exchange .
This interaction determines the evolution of the planet through changes to the orbital parameters .

Aims : We investigate changes in the orbital elements of a 20 Earth–mass planet due to the torques from the disk .
We focus on the non-linear evolution of initially non-vanishing eccentricity , e , and/or inclination , i .

Methods : We treat the disk as a two- or three-dimensional viscous fluid and perform hydrodynamical simulations using finite difference methods .
The planetary orbit is updated according to the gravitational torque exerted by the disk .
We monitor the time evolution of the orbital elements of the planet .

Results : We find rapid exponential decay of the planet orbital eccentricity and inclination for small initial values of e and i , in agreement with linear theory .
For larger values of e > 0.1 the decay time increases and the decay rate scales as \dot { e } \propto e ^ { -2 } , consistent with existing theoretical models .
For large inclinations ( i > 6 ^ { \circ } ) the inclination decay rate shows an identical scaling di / dt \propto i ^ { -2 } .
We find an interesting dependence of the migration on the eccentricity .
In a disk with aspect ratio H / r = 0.05 the migration rate is enhanced for small non-zero eccentricities ( e < 0.1 ) , while for larger values we see a significant reduction by a factor of \sim 4 .
We find no indication for a reversal of the migration for large e , although the torque experienced by the planet becomes positive when e \simeq 0.3 .
This inward migration is caused by the persisting energy loss of the planet .

Conclusions : For non gap forming planets , eccentricity and inclination damping occurs on a time scale that is very much shorter than the migration time scale .
The results of non linear hydrodynamic simulations are in very good agreement with linear theory for values of e and i for which the theory is applicable ( i.e . e and i \leq H / r ) .