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.
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