schroedinger_nonlinear_pde

schroedinger_nonlinear_pde, a MATLAB code which solves the complex partial differential equation (PDE) known as Schroedinger's nonlinear equation: dudt = i uxx + i gamma * |u|^2 u, in one spatial dimension, with Neumann boundary conditions.

This version of the problem illustrates how a fast soliton overtakes a slow one.

Licensing:

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

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

Source Code:

• schroedinger_nonlinear_conserved.m, evaluates a quantity that should be conserved.
• schroedinger_nonlinear_deriv.m, evaluates the right hand side of the ODE system.
• schroedinger_nonlinear_exact.m, evaluates the exact solution to the PDE.
• schroedinger_nonlinear_parameters.m, returns parameter values associated with the PDE.

• schroedinger_nonlinear_nonlinear_pde_test.m, calls all the tests.
• schroedinger_nonlinear_nonlinear_pde_test.sh, runs all the tests.
• schroedinger_nonlinear_nonlinear_pde_test.txt, the output file.

• schroedinger_nonlinear_midpoint.m, solves the nonlinear Schroedinger equation using midpoint.
• schroedinger_nonlinear_ode45.m, solves the nonlinear Schroedinger equation using ode45().

• midpoint.m, an implicit midpoint ODE solver.

• schroedinger_nonlinear_midpoint_initial.png, the solution at the initial time.
• schroedinger_nonlinear_midpoint_midway.png, the solution at the midway time.
• schroedinger_nonlinear_midpoint_final.png, the solution at the final time.

• schroedinger_nonlinear_ode45_initial.png, the solution at the initial time.
• schroedinger_nonlinear_ode45_midway.png, the solution at the midway time.
• schroedinger_nonlinear_ode45_final.png, the solution at the final time.