Nonlinear excitations in a compressible quantum Heisenberg Chain

We investigate both analytically and numerically non-linear coupled magnetic and elastic excitations of compressible Heisenberg Chains. From a shallow water wave treatment of perturbation terms. one can derive two types of coupled equations which are coupled Boussinesq and non-linear Schroedinger (NLS) equations arid coupled Boussinesq and NLS-like equations. We also simulate collisions between magnetic arid elastic solitons in the compressible Heisenberg chain when a nonlinearized approach is performed to deal with the magnetic modes in the presence of harmonic as well as anharmonic interactions. Finally from a Fast Fourier Transform (FFT) algorithm, the dynamical structure factor is computed for all the numerical solutions of the elastic mode for the model under consideration. (author)