  A nonlinear model of the scalar field with a coupling between the field and
its gradient is developed. It is shown, that such model is suitable for the
description of phase transition accompanied by formation of spatial
inhomogeneous distribution of the order parameter. The proposed model is
analogous the mechanical nonlinear oscillator with the coordinate-dependent
mass or velocity-dependent elastic module. Besides, for some value of energy
the model under consideration possesses exact analytical solution. We assume
that this model can related to the spinodal decomposition, quark confinement,
or cosmological scenario. All predictions can be verified experimentally.
