An Open-Source Pseudo-Spectral Solver for Idealized Korteweg-de Vries Soliton Simulations
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arXiv
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| Main Authors: | , , , , , , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866917299516080128 |
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| author | Irawan, Dasapta E. Herho, Sandy H. S. Khadami, Faruq Anwar, Iwan P. Sujatmiko, Karina A. Handayani, Alfita P. Fajary, Faiz R. Suwarman, Rusmawan |
| author_facet | Irawan, Dasapta E. Herho, Sandy H. S. Khadami, Faruq Anwar, Iwan P. Sujatmiko, Karina A. Handayani, Alfita P. Fajary, Faiz R. Suwarman, Rusmawan |
| contents | The Korteweg-de Vries (KdV) equation governs the propagation of nonlinear internal and surface gravity waves in shallow ocean environments, where the balance between nonlinear steepening and frequency-dependent dispersion produces solitons. This article presents sangkuriang, an open-source Python library that solves the KdV equation using Fourier pseudo-spectral spatial discretization and adaptive eighth-order Runge-Kutta time integration, accelerated via just-in-time (JIT) compilation. Validation across four progressively complex scenarios-isolated soliton propagation, symmetric interactions, overtaking collisions, and three-body interactions-demonstrates high-fidelity conservation of mass, momentum, and energy, with relative errors below $O(10^{-4})$. Measured soliton velocities agree with theoretical predictions within $5\%$, and complementary diagnostics based on spectral entropy and recurrence quantification analysis (RQA) confirm that computed solutions preserve the regular phase-space structure characteristic of integrable Hamiltonian systems. Running on a standard laptop, sangkuriang provides a robust, lightweight platform for reproducible numerical investigation of idealized nonlinear dispersive wave dynamics relevant to coastal and ocean engineering applications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_12029 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | An Open-Source Pseudo-Spectral Solver for Idealized Korteweg-de Vries Soliton Simulations Irawan, Dasapta E. Herho, Sandy H. S. Khadami, Faruq Anwar, Iwan P. Sujatmiko, Karina A. Handayani, Alfita P. Fajary, Faiz R. Suwarman, Rusmawan Pattern Formation and Solitons Numerical Analysis Atmospheric and Oceanic Physics Computational Physics Physics Education 35Q53, 65M70, 35C08, 37K40, 76B25 The Korteweg-de Vries (KdV) equation governs the propagation of nonlinear internal and surface gravity waves in shallow ocean environments, where the balance between nonlinear steepening and frequency-dependent dispersion produces solitons. This article presents sangkuriang, an open-source Python library that solves the KdV equation using Fourier pseudo-spectral spatial discretization and adaptive eighth-order Runge-Kutta time integration, accelerated via just-in-time (JIT) compilation. Validation across four progressively complex scenarios-isolated soliton propagation, symmetric interactions, overtaking collisions, and three-body interactions-demonstrates high-fidelity conservation of mass, momentum, and energy, with relative errors below $O(10^{-4})$. Measured soliton velocities agree with theoretical predictions within $5\%$, and complementary diagnostics based on spectral entropy and recurrence quantification analysis (RQA) confirm that computed solutions preserve the regular phase-space structure characteristic of integrable Hamiltonian systems. Running on a standard laptop, sangkuriang provides a robust, lightweight platform for reproducible numerical investigation of idealized nonlinear dispersive wave dynamics relevant to coastal and ocean engineering applications. |
| title | An Open-Source Pseudo-Spectral Solver for Idealized Korteweg-de Vries Soliton Simulations |
| topic | Pattern Formation and Solitons Numerical Analysis Atmospheric and Oceanic Physics Computational Physics Physics Education 35Q53, 65M70, 35C08, 37K40, 76B25 |
| url | https://arxiv.org/abs/2601.12029 |