.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/gallery_03/g_model_NSE.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        Click :ref:`here <sphx_glr_download_auto_examples_gallery_03_g_model_NSE.py>`
        to download the full example code

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_auto_examples_gallery_03_g_model_NSE.py:


Nonlinear Schrödinger equation -- Third-order soliton
=====================================================

This example solves the standard nonlinear Schrödinger equation, given by

.. math::
    \partial_z u = -i \frac{\beta_2}{2}\partial_t^2 u + i\gamma |u|^2 u,

wherein :math:`u = u(z, t)` represents the slowly varying pulse envelope,
:math:`\beta_2=-1` is the second order dispersion parameter, and
:math:`\gamma=1` is the nonlinear parameter.  As initial condition, a
higher-order soliton

.. math::
    u_0(t) = N_{\rm{sol}} \sqrt{\frac{|\beta_2|}{\gamma \, t_0^2}} {\rm{sech}}(t/t_0),

of duration :math:`t_0=1`, and soliton order :math:`N_{\rm{sol}}=3` is
considered. The propagation is performed up to :math:`z_{\rm{max}}=\pi/2`, i.e.
for one soliton period.

.. codeauthor:: Oliver Melchert <melchert@iqo.uni-hannover.de>

.. GENERATED FROM PYTHON SOURCE LINES 24-87



.. image:: /auto_examples/gallery_03/images/sphx_glr_g_model_NSE_001.png
    :alt: $|u|^2/{\rm{max}}\left(|u|^2\right)$, $|u_\omega|^2/{\rm{max}}\left(|u_\omega|^2\right)$
    :class: sphx-glr-single-img





.. code-block:: default

    import fmas
    import numpy as np
    from fmas.models import ModelBaseClass
    from fmas.config import FTFREQ, FT, IFT, C0
    from fmas.solver import SySSM
    from fmas.grid import Grid
    from fmas.tools import plot_evolution


    class NSE(ModelBaseClass):
        def __init__(self, w, b2 = -1.0, gamma = 1.0):
            super().__init__(w, 0.5*b2*w*w)
            self.gamma = gamma

        @property
        def Lw(self):
            return 1j*self.beta_w

        def Nw(self, uw):
            ut = IFT(uw)
            return 1j*self.gamma*FT(np.abs(ut)**2*ut)

        def claw(self, i, zi, w, uw):
            return np.sum(np.abs(uw)**2)


    def main():
        # -- DEFINE SIMULATION PARAMETERS
        # ... WAVEGUIDE PROPERTIES
        b2 = -1.0
        gamma = 1.
        # ... TEST PULSE PROPERTIES
        t0 = 1.                       # soliton duration
        P0 = np.abs(b2)/t0/t0/gamma   # peak-intensity
        LD = t0*t0/np.abs(b2)         # dispersion length
        N_sol = 3                     # soliton order
        # ... COMPUTATIONAL DOMAIN 
        t_max = 30.
        t_num = 2**12
        z_max  = 0.5*np.pi*LD
        z_num  = 1000
        z_skip = 2

        # -- INITIALIZATION STAGE
        # ... COMPUTATIONAL DOMAIN
        grid = Grid( t_max = t_max, t_num = t_num, z_max = z_max, z_num = z_num)
        # ... NSE MODEL 
        model = NSE(grid.w, b2, gamma)
        # ... Z-PROPAGATION USING SYMMETRIC SPLIT-STEP FOURIER METHOD 
        solver = SySSM(model.Lw, model.Nw)
        # ... INITIAL CONDITION
        u_0t = N_sol*np.sqrt(P0)/np.cosh(grid.t/t0)
        solver.set_initial_condition(grid.w, FT(u_0t))

        # -- RUN SIMULATION
        solver.propagate(z_range = z_max, n_steps = z_num, n_skip = z_skip)

        plot_evolution( solver.z, grid.t, solver.utz,
            t_lim = (-4,4), w_lim = (-50,50), DO_T_LOG=False)


    if __name__=='__main__':
        main()


.. rst-class:: sphx-glr-timing

   **Total running time of the script:** ( 0 minutes  1.374 seconds)


.. _sphx_glr_download_auto_examples_gallery_03_g_model_NSE.py:


.. only :: html

 .. container:: sphx-glr-footer
    :class: sphx-glr-footer-example



  .. container:: sphx-glr-download sphx-glr-download-python

     :download:`Download Python source code: g_model_NSE.py <g_model_NSE.py>`



  .. container:: sphx-glr-download sphx-glr-download-jupyter

     :download:`Download Jupyter notebook: g_model_NSE.ipynb <g_model_NSE.ipynb>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_