Structural stability of non-ground state traveling waves of coupled nonlinear Schrödinger equations

Abstract

We consider the linear stability and structural stability of non-ground state traveling waves of a pair of coupled nonlinear Schrödinger equations (CNLS) which describe the evolution of co-propagating polarized pulses in the presence of birefringence. Viewing the CNLS equations as a Hamiltonian perturbation of the Manakov equations, we find parameter regimes in which there are two stable families of traveling waves. The usual variational methods for stability analysis of ground states do not apply. Instead we employ a Liapunov-Schmidt type reduction to detect eigenvalues bifurcating from the imaginary axis. We also demonstrate the instability of a family of vector solitons.