Nonlinear excitations in a compressible quantum Heisenberg chain

We investigate, both analytically and numerically, nonlinearly 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 nonlinear Schrِdinger (NLS) equations and coupled Boussinesq and NLS-like equations. We also simulate collisions between magnetic and 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.