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Research Paper#Physics, Integrable Systems, Numerical Methods🔬 ResearchAnalyzed: Jan 3, 2026 19:26

Integrable Discretizations of Sine-Gordon in Non-Characteristic Coordinates

Published:Dec 28, 2025 13:20
1 min read
ArXiv

Analysis

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.
Reference

“The paper proposes integrable space discretizations of the sine-Gordon equation in three distinct cases of non-characteristic coordinates.”

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Research Paper#Physics, Numerical Simulation, Nonlinear Field Theory🔬 ResearchAnalyzed: Jan 3, 2026 19:48

amangkurat: A Python Library for Simulating Nonlinear Klein-Gordon Equation

Published:Dec 27, 2025 16:15
1 min read
ArXiv

Analysis

This paper introduces a new open-source Python library, amangkurat, for simulating the nonlinear Klein-Gordon equation. The library uses a hybrid numerical method (Fourier pseudo-spectral spatial discretization and a symplectic Størmer-Verlet temporal integrator) to ensure accuracy and long-term stability. The paper validates the library's performance across various physical regimes and uses information-theoretic metrics to analyze the dynamics. This work is significant because it provides a readily available and efficient tool for researchers and educators in nonlinear field theory, enabling exploration of complex phenomena.
Reference

“The library's capabilities are validated across four canonical physical regimes: dispersive linear wave propagation, static topological kink preservation in phi-fourth theory, integrable breather dynamics in the sine-Gordon model, and non-integrable kink-antikink collisions.”

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