schroedinger_linear_pde


schroedinger_linear_pde, a MATLAB code which solves the complex partial differential equation (PDE) known as Schroedinger's linear equation: dudt = i uxx, in one spatial dimension, with Neumann boundary conditions.

A soliton is a sort of wave solution to the equation which preserves its shape and moves left or right with a fixed speed. If two solitons are present, then as one overtakes the other, their shapes will merge and interfere for a certain time. This version of the problem illustrates how a fast soliton overtakes a slow one, moving from left to right.

Licensing:

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

Languages:

schroedinger_linear_pde is available in a MATLAB version.

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schroedinger_linear_pde_test

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References:

  1. Willem Hundsdorfer, Jan Verwer,
    Numerical solution of time-dependent advection-diffusion-reaction equations,
    Springer, 2003, page 128, page 209.
    ISBN: 978-3-662-09017-6
  2. https://eqworld.ipmnet.ru/
    Exact Solutions:
    Nonlinear Partial Differential Equations:
    Second-Order Parabolic Partial Differential Equations:
    Schrodinger Equation with a Cubic Nonlinearity

Source Code:


Last revised on 19 April 2021.