  Breather solutions are considered to be generally accepted models of rogue
waves. However, breathers are not localized, while wavefields in nature can
generally be considered as localized due to the limited spatial dimensions.
Hence, the theory of rogue waves needs to be supplemented with localized
solutions which evolve locally as breathers. In this paper, we present a
universal method for constructing such solutions from exact multi-soliton
solutions, which consists in replacing the plane wave in the dressing
construction of the breathers with a specific exact $N$-soliton solution
converging asymptotically to the plane wave at large number of solitons $N$. On
the example of the Peregrine, Akhmediev, Kuznetsov-Ma and Tajiri-Watanabe
breathers, we show that the constructed with our method multi-soliton
solutions, being localized in space with characteristic width proportional to
$N$, are practically indistinguishable from the breathers in a wide region of
space and time at large $N$. Our method makes it possible to build solitonic
models with the same dynamical properties for the higher-order rational and
super-regular breathers, and can be applied to general multi-breather
solutions, breathers on a nontrivial background (e.g., cnoidal waves) and other
integrable systems. The constructed multi-soliton solutions can also be
generalized to capture the spontaneous emergence of rogue waves through the
spontaneous synchronization of soliton norming constants, though finding these
synchronizations conditions represents a challenging problem for future
studies.
