Existence and stability of multi-pulses with applications to nonlinear optics.

Abstract: We study the existence and stability of multi-pulses in dynamical systems that arise as traveling-wave equations for a partial differential equation (PDE) with symmetries. We consider reversible, Z_2 symmetric dynamical systems with heteroclinic orbits related via symmetries. The heteroclinic orbits are assumed to undergo an orbit flip bifurcation upon changing appropriate parameters. We construct multi-bump solutions close to the heteroclinic orbits and investigate their PDE stability by using Lin's method and Lyapunov-Schmidt reduction. We apply this abstract theory to a model equation that describes the propagation of pulses in optical fibers with phase sensitive amplifiers. Our results show that stable multi-pulses exist.

This is a joint work with Bjorn Sandstede.