  Nonlinear phononics play important role in strong laser-solid interactions.
We discuss nonlinear dynamical protocols which allow for efficient excitation
and control of nonlinear phonons. We consider recent inspiring proposals:
inducing ferroelectricity in paraelectric material such as KTaO$_3$ and
inducing structural deformations in cuprates like La$_2$CuO$_4$ [A. Subedi
et.al, Phys. Rev. B 89,220301 (2014), A.Subedi, Phys. Rev. B 95, 134113
(2017)]. High-frequency phonon modes are driven by mid-infrared pulses, and
coupled to lower-frequency modes those indirect excitation causes structural
deformations. Such proposals are in line with a series of recent experiments on
light-induced phase transitions. We study in a more detail the case of KTaO$_3$
without strain, where (at first glance) it was not possible to excite the
needed low frequency phonon mode by resonant driving of the higher frequency
one. Behaviour of the phonon system is explained using a reduced model of
coupled driven nonlinear oscillators. We find a dynamical mechanism which
prevents effective excitation at resonance driving, and show that for certain
detunings of driving frequency from the exact resonance the system response is,
counterintuitively, greatly amplified. In order to induce ferroelectricity in
KTaO$_3$ without a strain we employ driving with sweeping frequency, realizing
so called capture into resonance. The method works for realistic femtosecond
pulses. Our approach can be applied to other related systems, e.g. laser driven
orthorombic perovskites like ErFeO$_3$.
