WELL-POSEDNESS OF NONLINEAR SCHRODINGER-AIRY TYPE EQUATION IN WEIGHTED SOBOLEV SPACES

Abstract

In this work, we start from the one-dimensional Dysthe equation and study its local well-posedness in Sobolev spaces. Previously, a similar equation, which we call a Nonlinear Schrodinger-Airy type, was proved to be well-posed in weighted Sobolev spaces, but with a constraint on coefficients, and now we improve the result by removing the constraint, but prove the well-posedness in a less regular weighted Sobolev space.