Dynamics of nonlinear wave equations in the vicinity of the bound states standing waves
by
Grozdena Todorova
University of Tennessee

We consider the dynamics of the Nonlinear Klein-Gordon equation( NLKG) and the Nonlinear Damped Wave equation( NLDWE) in the vicinity of the hight energy standing waves, so called bound states standing waves. The stability/instability problems for the least energy standing waves-ground state standing waves have been previously solved for the different types of evolution equations. Note that the difficulties which appear when we deal with the instability problem for bound states standing waves are much more complicated than those for the ground state standing waves.

Date received: December 20, 2002