kdv_exact, an Octave 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 = 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 information on this web page is distributed under the MIT license.
kdv_exact is available in a C version and a C++ version and a Fortran90 version and a MATLAB version and an Octave version and a Python version.
kdv_etdrk4, an Octave code which uses the exponential time differencing (ETD) RK4 method to solve the Korteweg-deVries (KdV) partial differential equation (PDE), by Aly-Khan Kassam, Lloyd Trefethen.
kdv_ift, an Octave code which uses the Inverse Fourier Transform (IFT) method to solve the Korteweg-deVries (KdV) partial differential equation (PDE), by Aly-Khan Kassam, Lloyd Trefethen.
octave_exact, an Octave code which evaluates exact solutions to a few selected examples of ordinary differential equations (ODE) and partial differential equations (PDE).