L. Berge, COALESCENCE AND INSTABILITY OF COPROPAGATING NONLINEAR-WAVES, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 58(5), 1998, pp. 6606-6625
An arbitrary number of light waves that collinearly propagate in a Ker
r cubic medium is investigated in the framework of n (n greater than o
r equal to 2) coupled nonlinear Schrodinger equations. Depending on th
eir initial separation distance and their power, the waves are shown t
o either disperse, collapse individually, or still attract each other
to form a central lobe that may blow up at a finite time. General resu
lts, including the fundamental relations that govern the wave centroid
s and their mean square radii, are established for two and more light
pulses. Their approximate evolution is described by means of a variati
onal approach applied to two Gaussian beams and theoretical arguments
detailing the attractor associated with the self-attraction of beams a
re 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 numbe
r 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. [S1063-651X(98)13910-7
].