Periodic multi-pulses and spectral stability in Hamiltonian PDEs with symmetry

Bifurcations of periodic orbits in the generalised nonlinear Schrödinger Equation

“…For a comprehensive presentation of the different types of connecting and homoclinic orbits and their symmetry properties we refer the reader to [2,3]. The overall message is that, in the same way, any other periodic orbit in the zero-energy level can be included in ever more complex heteroclinic cycles from and back to equilibrium 0 -to create a never ending menagerie of families of homoclinic orbits [15,18] and, hence, a huge variety of solitons of the GNLSE (1). This is why we next study the structure of periodic orbits of system (2) and how it changes with the parameter β 2 .…”