Nonlinear Schrödinger-Airy Equation in Sobolev Spaces of Low Regularity

Abstract

The Nonlinear Schrödinger-Airy equation is one of the general examples of dispersive nonlinear partial differential equations. It is commonly used to characterize the nonlinear propagation of light pulses in optical fibers and is of great importance in quantum mechanics. In this Capstone Project, we perform the first steps to show that the solution satisfies a priori upper bound in terms of the Hs(Sobolev Space) size of the initial data for -1/8 < s < 1/4 . The result is weaker than the well-posedness. The Capstone Project provides a general scheme of the ideas for the problem described above.