Spatial analyticity of solutions for a coupled system of generalized KdV equations

TL;DR

This paper proves that solutions to a coupled system of generalized KdV equations remain analytic over time, with the analyticity band narrowing at an algebraic rate, highlighting the persistence of regularity.

Contribution

It establishes the spatial analyticity of solutions for a coupled generalized KdV system and quantifies how the analyticity band shrinks over time.

Findings

Solutions remain analytic for all time.

The analyticity band width decreases algebraically over time.

Provides a quantitative measure of the loss of analyticity.

Abstract

The solution of a coupled system consisting of generalized Korteweg-de Vries-type equations is obtained for all time where the initial data are analytic on a band in the complex plane. We show that the width of this band decreases algebraically with time.