Nonlinear Integrable Equations and Nonlinear Fourier Transform

TL;DR

This paper explores the use of nonlocal functionals with homogeneous kernels to solve key nonlinear integrable equations like KdV, nonlinear Schrödinger, and Davey-Stewartson, advancing nonlinear Fourier analysis techniques.

Contribution

It introduces a novel approach employing nonlocal functionals with homogeneous kernels to address important nonlinear integrable equations.

Findings

Successfully applied nonlocal functionals to solve KdV, nonlinear Schrödinger, and Davey-Stewartson equations

Developed a framework connecting nonlocal functionals with nonlinear Fourier transforms

Enhanced analytical tools for nonlinear integrable systems

Abstract

In the paper we study nonlocal functionals whose kernels are homogeneous generalized functions. We also use such functionals to solve the Korteweg-de Vries , the nonlinear Schr\"odinger and the Davey-Stewartson equations.