  We report the results of ALMA 1-2 kpc-resolution, three rotational transition
line (J=2-1, J=3-2, and J=4-3) observations of multiple dense molecular gas
tracers (HCN, HCO$^{+}$, and HNC) for ten nearby (ultra)luminous infrared
galaxies ([U]LIRGs). Following the matching of beam sizes to 1-2 kpc for each
(U)LIRG, the high-J to low-J transition-line flux ratios of each molecule and
the emission line flux ratios of different molecules at each J transition are
derived. We conduct RADEX non-LTE model calculations and find that, under a
wide range of gas density and kinetic temperature, the observed
HCN-to-HCO$^{+}$ flux ratios in the overall (U)LIRGs are naturally reproduced
with enhanced HCN abundance compared to HCO$^{+}$. Thereafter, molecular gas
properties are constrained primarily through the use of HCN and HCO$^{+}$ data
and the adoption of fiducial values for the HCO$^{+}$ column density and
HCN-to-HCO$^{+}$ abundance ratio. We quantitatively confirm the following: (1)
Molecular gas at the (U)LIRGs' nuclei is dense ($\gtrsim$10$^{3-4}$ cm$^{-3}$)
and warm ($\gtrsim$100 K). (2) Molecular gas density and temperature in nine
ULIRGs' nuclei are significantly higher than that of one LIRG's nucleus. (3)
Molecular gas in starburst-dominated sources tends to be less dense and cooler
than ULIRGs with luminous AGN signatures. For six selected sources, we also
apply a Bayesian approach by freeing all parameters and support the above main
results. Our ALMA 1-2 kpc resolution, multiple transition-line data of multiple
molecules are a very powerful tool for scrutinizing the properties of molecular
gas concentrated around luminous energy sources in nearby (U)LIRGs' nuclei.
