amangkurat: A Python Library for Symplectic Pseudo-Spectral Solution of the Idealized (1+1)D Nonlinear Klein-Gordon Equation

TL;DR

The amangkurat Python library offers a symplectic pseudo-spectral solver for the (1+1)D nonlinear Klein-Gordon equation, enabling accurate, efficient simulations of various relativistic scalar field phenomena with advanced analysis tools.

Contribution

This work introduces amangkurat, a novel Python library combining spectral methods, symplectic integration, and adaptive techniques for robust Klein-Gordon simulations with comprehensive phenomenological analysis.

Findings

Validated across four physical regimes including solitons and kinks.

Achieves exponential spatial convergence and long-term Hamiltonian preservation.

Demonstrates high computational efficiency suitable for research and education.

Abstract

This study introduces amangkurat, an open-source Python library designed for the robust numerical simulation of relativistic scalar field dynamics governed by the nonlinear Klein-Gordon equation in $(1+1)$D spacetime. The software implements a hybrid computational strategy that couples Fourier pseudo-spectral spatial discretization with a symplectic St\o rmer-Verlet temporal integrator, ensuring both exponential spatial convergence for smooth solutions and long-term preservation of Hamiltonian structure. To optimize performance, the solver incorporates adaptive timestepping based on Courant-Friedrichs-Lewy (CFL) stability criteria and utilizes Just-In-Time (JIT) compilation for parallelized force computation. 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. Beyond standard numerical validation, this work establishes a multi-faceted analysis framework employing information-theoretic entropy metrics (Shannon, R\'{e}nyi, and Tsallis), kernel density estimation, and phase space reconstruction to quantify the distinct phenomenological signatures of these regimes. Statistical hypothesis testing confirms that these scenarios represent statistically distinguishable dynamical populations. Benchmarks on standard workstation hardware demonstrate that the implementation achieves high computational efficiency, making it a viable platform for exploratory research and education in nonlinear field theory.