Optical solitons with power-law asymptotics

It is shown that self-guided optical beams with power-law asymptotics, i.e., algebraic optical solitons, can be regarded as a special case of sech-type solitons (i.e. solitons with exponentially decaying asymptotics) in the limit where the beam propagation constant coincides with the threshold for linear wave propagation. This leads to the conjecture that algebraic optical solitons should be inherently unstable due to interactions with linear waves, even in cases when the corresponding family of sech-type solitons is stable. This conjecture is verified numerically for a wide class of optical solitons described by the generalized nonlinear Schr\"odinger equation with two competing nonlinearities. {} 1996 The American Physical Society.