Аннотация:
The higer order Nonlinear Schrödinger equation is one of the general
examples of dispersive nonlinear partial differential equations. We study a priori
bounds for higher-order nonlinear Schrödinger in the Sobolev space. The equation
models propagation of light pulses in optical fibers. We show that the solution
of the Cauchy problem associated with this equation solution satisfies a priori
upper bound which depends only on the time. The result is weak than the global
well-posedness. We obtain a priori bound on range −1/8 < s < 0. The main
methodology comes from recent work of Christ, Holmer and Tataru