SOLITONS AND THEIR STABILITY IN HIGH DISPERSIVE SYSTEMS .1. FOURTH-ORDER NONLINEAR SCHRODINGER-TYPE EQUATIONS WITH POWER-LAW NONLINEARITIES

摘要

The existence and stability of the soliton solutions to the fourth order nonlinear Schrodinger equations with nonlinear terms psi(2p)psi are studied numerically in one space dimension and compared with the analytical results. The solitons appear to be stable at p = 1, 2. At p = 3 an instability gives rise to the formation of periodically modulated pulse-like structures. At p greater than or equal to 4 the instability leads to the blowup. The results are in agreement with analytical predictions, obtained earlier [V.I. Karpman, Phys. Rev. E 53 (1996) R1336; Phys. Lett. A 215 (1996) 254]. (C) 1997 Elsevier Science B.V. [References: 12]