kdv_exact, a Fortran90 code which evaluates exact solutions 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 = 0
for which an exact solution is
u(x,t) = - 1/2 v ( sech ( 1/2 * sqrt ( v ) * ( x - v * t - a ) )^2
where parameter "a" is an arbitrary phase, and "v" represents
the wave velocity.
The information on this web page is distributed under the MIT license.
kdv_exact is available in a Fortran90 version and a MATLAB version and an Octave version and a Python version.
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