Coalescence and instability of copropagating nonlinear waves

An arbitrary number of light waves that collinearly propagate in a Kerr cubic medium is investigated in the framework of n $(n>~2)$ coupled nonlinear Schr\"odinger equations. Depending on their initial separation distance and their power, the waves are shown to either disperse, collapse individually, or still attract each other to form a central lobe that may blow up at a finite time. General results, including the fundamental relations that govern the wave centroids and their mean square radii, are established for two and more light pulses. Their approximate evolution is described by means of a variational approach applied to two Gaussian beams and theoretical arguments detailing the attractor associated with the self-attraction of beams are also given. Furthermore, an instability criterion for coupled bound states is derived using perturbation theory. It is shown that coupled stationary-wave solutions are unstable when the space dimension number is higher than 2, while their corresponding ground states are stable at lower dimension. Finally, the competition between the modulational instability of coupled waves and their natural tendency to amalgamate into one self-focusing structure is discussed.