Operator splitting for dispersion-generalized Benjamin-Ono equations

TL;DR

This paper analyzes operator splitting methods for a class of nonlinear equations including KdV, Benjamin-Ono, and Burgers, establishing first- and second-order convergence results in Sobolev spaces.

Contribution

It provides the first rigorous convergence analysis of Godunov and Strang splitting methods for dispersion-generalized Benjamin-Ono equations.

Findings

First-order convergence of Godunov splitting in Sobolev space

Second-order convergence of Strang splitting in Sobolev space

Applicable to a broad class of nonlinear dispersive equations

Abstract

We consider the operator splitting for a class of nonlinear equation, which includes the KdV equation, the Benjamin-Ono equation, and the Burgers equation. We prove a first-order approxomation in $\Delta t$ in the Sobolev space for the Godunov splitting, and second-order approximation for the Strang splitting.