<simulation xmds-version="2">
  <name>sech_soliton</name>
  
  <author>Sebastian Wuster / Graham Dennis</author>
  <description>
    Nonlinear Schrodinger equation with attractive interactions.
    This equation has an analytic solution of the form of a breathing soliton.
  </description>
  
  <geometry>
    <propagation_dimension> t </propagation_dimension>
    <transverse_dimensions>
      <dimension name="x" lattice="4096"  domain="(-4.0, 4.0)" />
    </transverse_dimensions>
  </geometry>
  
  <features>
    <auto_vectorise />
    <fftw />
    <globals>
      <![CDATA[
      const double N = 3.0;
      ]]>
    </globals>
  </features>
  
  <vector name="wavefunction" initial_basis="x" type="complex">
    <components>psi</components>
    <initialisation>
      <![CDATA[
        psi = N/cosh(x);
      ]]>
    </initialisation>
  </vector>
  
  <sequence>
    <integrate algorithm="ARK45" interval="1.570796327" tolerance="1e-6">
      <samples>200</samples>
      <operators>
        <operator kind="ip">
          <operator_names>L</operator_names>
          <![CDATA[
            L = -0.5*i*kx*kx;
          ]]>
        </operator>
        <integration_vectors>wavefunction</integration_vectors>
        <![CDATA[
          dpsi_dt = L[psi] + i*mod2(psi)*psi;
        ]]>
      </operators>
    </integrate>
  </sequence>
  
  <output>
      <sampling_group basis="x(512)" initial_sample="yes">
        <moments>density</moments>
        <dependencies>wavefunction</dependencies>
        <![CDATA[
          density = mod2(psi);
        ]]>
      </sampling_group>
  </output>
</simulation>