SOLITONS AND THEIR STABILITY IN HIGH DISPERSIVE SYSTEMS .1. 4TH-ORDERNONLINEAR SCHRODINGER-TYPE EQUATIONS WITH POWER-LAW NONLINEARITIES

The existence and stability of the soliton solutions to the fourth ord er nonlinear Schrodinger equations with nonlinear terms \psi\(2p)psi a re studied numerically in one space dimension and compared with the an alytical results. The solitons appear to be stable at p = 1, 2. At p = 3 an instability gives rise to the formation of periodically modulate d pulse-like structures. At p greater than or equal to 4 the instabili ty leads to the blowup. The results are in agreement with analytical p redictions, obtained earlier [V.I. Karpman, Phys. Rev. E 53 (1996) R13 36; Phys. Lett. A 215 (1996) 254]. (C) 1997 Elsevier Science B.V.