  We study the couplings between collective vibrations such as the isovector
giant dipole and isoscalar giant quadrupole resonances in tin isotopes in the
framework of the time-dependent Hartree-Fock theory with a Skyrme energy
density functional. These couplings are a source of anharmonicity in the
multiphonon spectrum. In particular, the residual interaction is known to
couple the isovector giant dipole resonance with the isoscalar giant quadrupole
resonance built on top of it, inducing a nonlinear evolution of the quadrupole
moment after a dipole boost. This coupling also affects the dipole motion in a
nucleus with a static or dynamical deformation induced by a quadrupole
constraint or boost respectively. Three methods associated with these different
manifestations of the coupling are proposed to extract the corresponding matrix
elements of the residual interaction. Numerical applications of the different
methods to 132Sn are in good agreement with each other. Finally, several tin
isotopes are considered to investigate the role of isospin and mass number on
this coupling. A simple 1/A dependence of the residual matrix elements is found
with no noticeable contribution from the isospin. This result is interpreted
within the Goldhaber-Teller model.
