An exponential-type integrator for the KdV equation

TL;DR

This paper presents a new exponential-type integrator for the KdV equation, demonstrating first-order convergence in H^1 for initial data in H^3, and discusses extending it to second-order accuracy.

Contribution

The paper introduces a novel exponential-type integrator for the KdV equation with proven convergence and outlines its potential for higher-order methods.

Findings

First-order convergence in H^1 for initial data in H^3.

The method is applicable to the KdV equation.

Potential extension to second-order accuracy.

Abstract

We introduce an exponential-type time-integrator for the KdV equation and prove its first-order convergence in $H^1$ for initial data in $H^3$. Furthermore, we outline the generalization of the presented technique to a second-order method.