<simulation xmds-version="2">
  <name> nonlinear_SE </name>
  
  <features>
    <benchmark />
    <auto_vectorise />
    <globals>
      <![CDATA[
        real N = 10.0; // number of atoms
        real g = 1.0;  // nonlinear coupling
      ]]>
    </globals>
  </features>
  
  <geometry>
    <propagation_dimension> t </propagation_dimension>
    <transverse_dimensions>
      <dimension name="x" lattice="512"
                 domain="(0, 7)" transform="dct"/>
    </transverse_dimensions>
  </geometry>

  <vector name="potential" type="real">
    <components> V </components>
    <initialisation>
      <![CDATA[
        V = 0.5*x*x;
      ]]>
    </initialisation>
  </vector>
  
  <vector name="wavefunction" type="complex">
    <components> psi </components>
    <initialisation>
      <![CDATA[
        psi = sqrt(N) * pow(M_PI, -0.25) * exp(-x*x/2);
      ]]>
    </initialisation>
  </vector>

  <sequence>
    <integrate algorithm="ARK45" interval="6.28" 
                                 tolerance="1e-5">
      <samples> 50 </samples>
      <operators>

        <operator kind="ip">
          <operator_names> T </operator_names>
          <![CDATA[
            T = -i * 0.5 * kx * kx;
          ]]>
        </operator>

        <integration_vectors>
          wavefunction
        </integration_vectors> 
        <dependencies> potential </dependencies>
        <![CDATA[
          dpsi_dt = T[psi] - i * (V + g * mod2(psi)) * psi;
        ]]>
      </operators>
    </integrate>
  </sequence>

  <output format="hdf5">
    <sampling_group initial_sample="yes" basis="x">
      <dependencies> wavefunction </dependencies>
      <moments> psireal psiimag </moments>
      <![CDATA[
        psireal = Re(psi);
        psiimag = Im(psi);
      ]]>
    </sampling_group>
  </output>
</simulation>
