2026/01/17 by Dasapta E. Irawan, Sandy H. S. Herho, Faruq Khadami +5 · 1 voice
Mathematics · Physics and Astronomy · #math.NA #nlin.PS #physics.ao-ph #physics.comp-ph #physics.ed-ph
paper · pdf · doi:10.3390/w18070779
arxiv published 2026/01/17 · arxiv updated 2026/02/27
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.
simple-idealized-1d-nlse: Pseudo-Spectral Solver for the 1D Nonlinear Schrödinger Equation