Nonlinear integral equations for finite volume excited state energies of the O(3) and O(4) nonlinear sigma-models

We propose nonlinear integral equations for the finite volume one-particle energies in the O(3) and O(4) nonlinear sigma-models. The equations are written in terms of a finite number of components and are therefore easier to solve numerically than the infinite component excited state TBA equations proposed earlier. Results of numerical calculations based on the nonlinear integral equations and the excited state TBA equations agree within numerical precision.