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The solitonic structures in ultradilute quantum liquid and Er-doped waveguide are
investigated in my thesis, dealing with their fundamental characteristics and dynamical
behaviour. In ultradilute quantum liquid, quantum fluctuations and interatomic
interactions coalesce to stabilize self-bound structures, such as quantum droplets (QD)
and quantum bubbles (QB). These structures exhibit soliton-like characteristics,
resulting from the balance of cubic and quadratic nonlinearities. The study employs
modulation instability (MI) analysis to delineate the parameter domains for the existence
of solitonic structures and matter-wave soliton trains. It is shown that the unique
configurations of kink-antikink pair uncover the dynamics of QD and QB. In addition, the
dynamical structure factor is used to provide a comprehensive study of the internal
modes of solitonic structures. In the context of nonlinear photonics, Erbium-doped
waveguide with cubic nonlinearity and three-level atomic coherence provide an ideal
testbed for the generation and manipulation of solitonic structures. The work examines
periodic solitonic pulses modeled by Jacobi elliptic functions, highlighting the interplay of
cubic nonlinearity and atomic coherence in shaping and amplifying ultrashort optical
pulses. Solitonic pulses yield the soliton molecules with an appropriate tuning of
nonlinearity and atomic coherence. This dual investigation bridges quantum liquid and
Er-doped waveguide, offering new insights into soliton dynamics and expanding their
applicability in modern physics and photonic technologies. |