  We derive and investigate several hydrodynamic formalisms that emerge from a
system of classical, ultra-relativistic scalar particles self-interacting via a
quartic potential. The specific form of the total cross-section enables the
analytical computation of all transport coefficients that appear in
Navier-Stokes (NS), Bemfica-Disconzi-Noronha-Kovtun (BDNK), and second-order
transient hydrodynamic theories. We solve all these formalisms in a Bjorken
flow scenario and show that NS and BDNK theories display unphysical features
when gradients become sufficiently large. This implies that these hydrodynamic
approaches may not be suitable to describe the early stages of heavy ion
collisions.
