<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>