kdv_exact


kdv_exact, an Octave 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 = 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.

Licensing:

The computer code and data files described and made available on this web page are distributed under the MIT license

Languages:

kdv_exact is available in a MATLAB version and an Octave version and a Python version.

Related Data and codes:

kdv_exact_test

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.

pendulum_nonlinear_exact, an Octave code which evaluates an exact formula for the solution of the the ordinary differential equations (ODE) that represent the behavior of a nonlinear pendulum of length L under a gravitational force of strength G.

navier_stokes_2d_exact, an Octave code which evaluates an exact solution to the incompressible time-dependent Navier-Stokes equations (NSE) over an arbitrary domain in 2D.

navier_stokes_3d_exact, an Octave code which evaluates an exact solution to the incompressible time-dependent Navier-Stokes equations (NSE) over an arbitrary domain in 3D.

stokes_2d_exact, an Octave code which evaluates exact solutions to the incompressible steady Stokes equations over the unit square in 2D.

Reference:

Source Code:


Last revised on 15 November 2023.