  We introduce a variational method for calculating dispersion relations of
translation invariant (1+1)-dimensional quantum field theories. The method is
based on continuous matrix product states and can be implemented efficiently.
We study the critical Lieb-Liniger model as a benchmark and excelent agreement
with the exact solution is found. Additionally, we observe solitonic signatures
of Lieb's Type II excitation. In addition, a non-integrable model is introduced
where a U(1)-symmetry breaking term is added to the Lieb-Liniger Hamiltonian.
For this model we find evidence of a non-trivial bound-state excitation in the
dispersion relation.
