Modulated phases as variational solutions in liquid-crystalline systems

A variational approach is employed to search for exact solutions describing the director profile in the framework of an extended Frank elastic energy density. This extension of the energy density of the usual nematic phase adds an extra element of symmetry represented by the axis t, thus augmenting the number of possible phases described by the elastic energy, which includes modulated phases. The solutions corresponding to these phases are searched by exploring the symmetry properties and the existence of conserved quantities, which permits us to reduce the general solution of the variational problem to quadratures. This approach may be particularly useful to investigate the existence and stability of the recently discovered twist-bend nematic phase as well as to predict the orientational properties of other periodically