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Structure of the Moving Soliton in the TLM Model

A moving soliton solution is obtained analytically in the TLM model. We assume that the order parameter is a function of x - v t , v being the soliton velocity. This assumption is later verified. The equations of motion for the electronic wave function and the order parameter are solved with the help of the perturbation method, v being the small parameter. In the first order, there is no correction to the TLM order parameter. The wave functions are modulated. In the second order, the correction to the order parameter is calculated numerically. The corrected moving soliton presents a width contraction as the soliton velocity increases. A contraction of about 10% is found at the maximum velocity. The obtained results are compared with the form determined by numerical simulation works. The second order correction of the wave functions is also numerically calculated. Corrections to the kinetic, lattice potential, and electronic energies are calculated and their implications discussed.