Stability and dynamical features of solitary wave solutions for a hydrodynamic-type system taking into account nonlocal effects

• Hydrodynamic system taking into account non-local effects is proposed.
• The modeling system is shown to be non-integrable.
• Conditions are stated assuring the existence of soliton-like solutions.
• Stability of the soliton-like solutions is analyzed.
• Soliton-like solutions are shown to possess some features of “true” solitons.

We consider a hydrodynamic-type system of balance equations for mass and momentum closed by the dynamical equation of state taking into account the effects of spatial nonlocality. We study higher symmetry admitted by this system and establish its non-integrability for the generic values of parameters. A system of ODEs obtained from the system under study through the group theory reduction is investigated. The reduced system is shown to possess a family of the homoclinic solutions describing solitary waves of compression and rarefaction. The waves of compression are shown to be unstable. On the contrary, the waves of rarefaction are likely to be stable. Numerical simulations reveal some peculiarities of solitary waves of rarefaction, and, in particular, the recovery of their shape after the collisions.