Structure-preserving integrators for the Benjamin-type equations

TL;DR

This paper introduces new structure-preserving numerical integrators for Benjamin-type equations, which are non-local PDEs involving the Hilbert transform, demonstrating their effectiveness through numerical experiments.

Contribution

The paper proposes a novel reformulation and discretization approach for Benjamin-type equations, enhancing structure preservation in numerical integration.

Findings

Numerical experiments confirm the effectiveness of the proposed integrators.

The new methods better preserve the equations' structure compared to existing approaches.

Abstract

The numerical integration of the Benjamin and Benjamin--Ono equations are considered. They are non-local partial differential equations involving the Hilbert transform, and due to this, so far quite few structure-preserving integrators have been proposed. In this paper, a new reformulation of the equations is stated, and new structure-preserving discretizations are proposed based on it. Numerical experiments confirm the effectiveness of the proposed integrators.