  The description of strongly-correlated quantum many-body systems far-from
equilibrium is intrinsically challenging due to the amount of information it
requires. We introduce a generalization of the Jastrow ansatz for
time-dependent wavefunctions, that provides an efficient and exact description
of the time-evolution of a variety of systems exhibiting strong correlations.
Exact solutions previously known are characterized by scale invariance, making
the evolution of local correlations, such as the spatial density, self-similar.
However, we find that a complex-valued time-dependent Jastrow ansatz (TDJA) is
not restricted to scale-invariance and can describe processes lacking it. The
associated time evolution is equivalent to the implementation of a shortcut to
adiabaticity (STA) by counterdiabatic driving along a continuous manifold of
quantum states described by a real-valued TDJA. Thus, our results provide the
means to engineer exact STA in strongly-correlated many-body quantum systems
lacking scale invariance. We illustrate our findings in systems with
inverse-square interactions, such as the Calogero-Sutherland and the hyperbolic
models, that are supplemented with pairwise logarithmic interactions. We
further consider the dynamics of bosons subject to both contact and Coulomb
interactions in one dimension, known as the long-range Lieb-Liniger model. Our
results can be used to study the quench dynamics in all these models. Our
findings provide a benchmark for numerical and quantum simulations of
nonequilibrium strongly-correlated systems with continuous variables.
