Global dynamics of the generalized fifth-order KdV equation with critical nonlinearity

TL;DR

This paper establishes global existence and modified scattering for solutions to a generalized fifth-order KdV equation with critical nonlinearity, using advanced analytical techniques for small, localized initial data.

Contribution

It introduces a rigorous proof of global behavior and scattering for a complex nonlinear PDE with critical nonlinearity, employing space-time resonance and stationary phase methods.

Findings

Proves global existence for small, localized initial data.

Demonstrates modified scattering behavior.

Utilizes space-time resonance and stationary phase techniques.

Abstract

We prove global existence and modified scattering for the solutions of the generalized fifth-order KdV equation with critical nonlinearity for small and localized initial data. The proof is undergoing by using the space-time resonance method and the stationary phase argument.