1. Existence and Stability of Discrete Breathers in a Hexagonal Lattice Application in a Dusty Plasma Crystal V. Koukouloyannis, I. Kourakis Hamiltonian Lattice Dynamical Systems Leiden, October 2007

2. Existence of 3-site breathers in a Hexagonal Lattice This system is described by the Hamiltonian Consider the phase differences (VK and R.S.MacKay, J. Phys. A, 38 (2005) 1021-1030) This system supports 3-site breathers if where Since which always has the solutions

3. Hamiltonian Lattice Dynamical Systems Leiden, October 2007 The single-site breather Up to tree moving sites there are four cases of breathers Case (a): Single site breather

4. Hamiltonian Lattice Dynamical Systems Leiden, October 2007 The 3-site breathers Case (b): In-phase 3-site breather Linear stability condition for small ε:

5. Hamiltonian Lattice Dynamical Systems Leiden, October 2007 The 3-site breathers Case (c): Out of phase 3-site breather Linear stability condition for small ε:and

6. Hamiltonian Lattice Dynamical Systems Leiden, October 2007 The 3-site breathers Condition for linear stability for small ε: Case (d):Vortex 3-site breather with

7. Hamiltonian Lattice Dynamical Systems Leiden, October 2007 The dusty plasma crystal Table 1: Values suggested by A. Melzer abε set I0.01-0.040.034 set II0.01-0.060.065 set III-0.21-0.020.17 The transverse displacement is described by the Klein-Gordon Hamiltonian with ε<0 (inverse dispersion) and Since and the vortex breather are unstable even for small ε., the out of phase For set I the single and the in phase breathers can be continued for large enough ε so the system can support them.