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arXiv · 2010.16005

Well-posedness for a modified nonlinear Schrodinger equation modeling the formation of rogue waves

Curtis Holliman·Logan Hyslop
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Abstract

The Cauchy problem for a higher order modification of the nonlinear Shcrodinger equation (MNLS) on the line is shown to be well-posed in Sobolev spaces with exponent $\ge 0$. This result is achieved by demonstrating that the associated integral operator is a contraction on a Bourgain space that has been adapted to the particular linear symbol present in the equation. the ctraction is proved by using microlocal analysis and a new trilinear estimate.

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Curtis Holliman, Logan Hyslop. 2020-10-30. Well-posedness for a modified nonlinear Schrodinger equation modeling the formation of rogue waves. https://arxiv.org/abs/2010.16005

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