  Recent experiments on walking droplets suggest an underlying connection
between fluid dynamics and the quantum mechanics. Such experiments may be used
to support the de Broglie-Bohm pilot-wave theory. In this paper we show that
many quantum-like features of hydrodynamic excitations can be explained in the
framework of the parametrically driven nonlinear Schr\"{o}dinger equation
(DNLSE). It is shown that the nonlinear Schr\"{o}dinger equation (NLSE)
describes the pseudoquantum features of a given pseudoparticle in the Sagdeev
pseudopotential just as the ordinary linear Schr\"{o}dinger equation (LSE)
describes the quantum nature of real particles. The NLSE is shown to reduce to
nonlinear Hamilton-Jacobi equation (NHJE) for the phase function of the complex
wavefunction. The origin of the wave-particle dual-character in both LSE and
NLSE is explained and basic similarities between the two models is highlighted.
It is shown that many more pseudoquantum effects (yet to be explored) such as
pseudoentanglement, self-interference effect and quantization of pseudoparticle
energy are inherent features of classical fluids. Current investigation
suggests that emergence of the quantum nature of fluids is independent from
dynamics of the bouncing droplets or their interactions with the surface waves
instantaneously created by them. In contrast to previous suggestions, it is
remarked that intrinsically nonlinear collective excitations of a fluid can
drive any particle even a pseudoparticle to behave quantum mechanically. These
collective interactions in hydrodynamic model confirm the important nonlocal
character (which is a key aspect of the de Broglie-Bohm pilot-wave theory) of
all the pseudoquantum phenomena. The recent hydrodynamic quantum analog
experiments and extensive new theoretical models may hopefully enable
physicists to unlock the decade long hidden mystery of the quantum weirdness.
