<?xml version="1.0" encoding="UTF-8"?>
<simulation xmds-version="2">
  <name>nlse</name>

  <author>Joe Hope</author>
  <description>
    The nonlinear Schrodinger equation in one dimension, 
    which is a simple partial differential equation.  
    We introduce several new features in this script.
  </description>

  <features>
      <benchmark />
      <bing />
      <fftw plan="patient" />

      <auto_vectorise />
      <globals>
          <![CDATA[
          const double energy = 4;
          const double vel = 0.3;
          const double hwhm = 1.0;
          ]]>
       </globals>
     </features>

  <geometry>
      <propagation_dimension> xi </propagation_dimension>
      <transverse_dimensions>
        <dimension name="tau" lattice="128"  domain="(-6, 6)" />
      </transverse_dimensions>
   </geometry>

  <vector name="wavefunction" type="complex" dimensions="tau">
    <components> phi </components>
    <initialisation>
      <![CDATA[
      const double w0 = hwhm*sqrt(2/log(2));
      const double amp = sqrt(energy/w0/sqrt(M_PI/2));
      phi = amp*exp(-tau*tau/w0/w0)*exp(i*vel*tau);
      ]]>
    </initialisation>
  </vector>

  <vector name="dampingVector" type="real">
    <components> Gamma </components>
    <initialisation>
      <![CDATA[
      Gamma=1.0*(1-exp(-pow(tau*tau/4.0/4.0,10)));
      ]]>
    </initialisation>
  </vector>

  <sequence>
    <integrate algorithm="ARK45" interval="20.0" tolerance="1e-7">
      <samples>10 100 10</samples>
      <operators>
        <integration_vectors>wavefunction</integration_vectors>
        <operator kind="ex">
          <operator_names>Ltt</operator_names>
          <![CDATA[
            Ltt = -i*ktau*ktau*0.5;
          ]]>
        </operator>
        <![CDATA[
        dphi_dxi = Ltt[phi] - phi*Gamma + i*mod2(phi)*phi;
        ]]>
        <dependencies>dampingVector</dependencies>
      </operators>
    </integrate>
  </sequence>

  <output>
      <sampling_group basis="tau" initial_sample="yes">
        <moments>density</moments>
        <dependencies>wavefunction</dependencies>
        <![CDATA[
          density = mod2(phi);
        ]]>
      </sampling_group>

      <sampling_group basis="tau(0)" initial_sample="yes">
        <moments>normalisation</moments>
        <dependencies>wavefunction</dependencies>
        <![CDATA[
          normalisation = mod2(phi);
        ]]>
      </sampling_group>

      <sampling_group basis="ktau(32)" initial_sample="yes">
        <moments>densityK</moments>
        <dependencies>wavefunction</dependencies>
        <![CDATA[
          densityK = mod2(phi);
        ]]>
      </sampling_group>

  </output>
</simulation>