kdv_exact, a Python code which evaluates an exact solution of the Korteweg-deVries (KdV) partial differential equation (PDE) that represents the motion of a soliton.
The equation for u(x,t), the height of the wave, has the form
ut - 6 u ux + uxxx = 0for which an exact solution is
u(x,t) = - 1/2 v ( sech ( 1/2 * sqrt ( v ) * ( x - v * t - a ) )^2where parameter "a" is an arbitrary phase, and "v" represents the wave velocity.
The computer code and data files described and made available on this web page are distributed under the MIT license
kdv_exact is available in a MATLAB version and an Octave version and a Python version.
navier_stokes_2d_exact, a MATLAB code which evaluates an exact solution to the incompressible time-dependent Navier-Stokes equations (NSE) over an arbitrary domain in 2D.
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