  Exceptional points are a ubiquitous concept widely present in
driven-dissipative coupled systems described by a non-Hermitian Hamiltonian. It
is characterized by the degeneracy of the Hamiltonian's eigenvalues and
coalescence of corresponding eigenvectors. Recent developments demonstrated
that exceptional points can play an important role in photonics. However, to
date, exceptional points have been extensively examined in the systems
supporting only a few optical modes, thereby leaving the observation of
collective (multimode) effects outside of the scope of study. In the present
paper, we analyze the role of exceptional points in nonlinear multimode
photonics. Specifically, we provide insights into complex nonlinear dynamics
arising in a continuous wave-driven pair of strongly coupled nonlinear
micro-resonators (i.e. a nonlinear photonic dimer) operating in the multimode
regime. Investigating this system, which is known to possess exceptional
points, we find two fundamentally different nonlinear regimes of operation
corresponding to effective parity-time symmetric and broken parity-time
symmetry states. We demonstrate that the photonic dimer can be critically
coupled to a bus waveguide, thereby, providing an efficient generation of the
dissipative Kerr solitons on both sides of the exceptional point. The
parity-time symmetric case, which corresponds to a pair of symmetrically split
resonances, has been recently shown to exhibit a variety of emergent phenomena
including gear soliton generation, symmetry breaking, and soliton hopping.
Dissipative solitons generation in the parity-time symmetry broken case -
leading to the dissipation splitting - up to now remains unexplored.
