General, templated implementation of an order 2 semi-implicit Adams Bashforth/backward‐differentiation time stepping scheme and an order 2 exponential Runge-Kutta method applied to a spectral discretization in space of the Korteweg–de Vries equation with smooth initial data and periodic boundary conditions.
The implementation is built on top of Eigen and Eigen's wrapper around FFTW. A C++ binding to Python's matplotlib API is also included for visualization purposes.
The methods and application are summarized in the pdf document. Below is a short animation depicting two solitons passing through each other, after which they recover their original shapes.
