This book explores the diverse types of Schroedinger equations that
appear in nonlinear systems in general, with a specific focus on
nonlinear transmission networks and Bose-Einstein Condensates. In
the context of nonlinear transmission networks, it employs various
methods to rigorously model the phenomena of modulated matter-wave
propagation in the network, leading to nonlinear Schroedinger (NLS)
equations. Modeling these phenomena is largely based on the
reductive perturbation method, and the derived NLS equations are
then used to methodically investigate the dynamics of matter-wave
solitons in the network. In the context of Bose-Einstein
condensates (BECs), the book analyzes the dynamical properties of
NLS equations with the external potential of different types, which
govern the dynamics of modulated matter-waves in BECs with either
two-body interactions or both two- and three-body interatomic
interactions. It also discusses the method of investigating both
the well-posedness and the ill-posedness of the boundary problem
for linear and nonlinear Schroedinger equations and presents new
results. Using simple examples, it then illustrates the results on
the boundary problems. For both nonlinear transmission networks and
Bose-Einstein condensates, the results obtained are supplemented by
numerical calculations and presented as figures.
General
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