Integrable Discretizations of Sine-Gordon in Non-Characteristic Coordinates

This paper addresses the problem of discretizing the sine-Gordon equation, a fundamental equation in physics, in non-characteristic coordinates. It contrasts with existing work that primarily focuses on characteristic coordinates. The paper's significance lies in exploring new discretization methods, particularly for laboratory coordinates, where the resulting discretization is complex. The authors propose a solution by reformulating the equation as a two-component system, leading to a more manageable discretization. This work contributes to the understanding of integrable systems and their numerical approximations.