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Breather solutions are considered to be generally accepted models of roguewaves. However, breathers are not localized, while wavefields in nature cangenerally be considered as localized due to the limited spatial dimensions.Hence, the theory of rogue waves needs to be supplemented with localizedsolutions which evolve locally as breathers. In this paper, we present auniversal method for constructing such solutions from exact multi-solitonsolutions, which consists in replacing the plane wave in the dressingconstruction of the breathers with a specific exact $N$-soliton solutionconverging asymptotically to the plane wave at large number of solitons $N$. Onthe example of the Peregrine, Akhmediev, Kuznetsov-Ma and Tajiri-Watanabebreathers, we show that the constructed with our method multi-solitonsolutions, being localized in space with characteristic width proportional to$N$, are practically indistinguishable from the breathers in a wide region ofspace and time at large $N$. Our method makes it possible to build solitonicmodels with the same dynamical properties for the higher-order rational andsuper-regular breathers, and can be applied to general multi-breathersolutions, breathers on a nontrivial background (e.g., cnoidal waves) and otherintegrable systems. The constructed multi-soliton solutions can also begeneralized to capture the spontaneous emergence of rogue waves through thespontaneous synchronization of soliton norming constants, though finding thesesynchronizations conditions represents a challenging problem for futurestudies.

Multisoliton interactions approximating the dynamics of breather solutions