Multidimensional ion-acoustic solitary waves and shocks in quantum plasmas

•Solitary waves and shocks (SWS) can propagate in quantum electron–ion plasmas.•Small-amplitude SWS become compressive (rarefactive) when H<(>)2/3H<(>)2/3.•Large-amplitude SWS exist only of the compressive type.•Oscillatory shocks transit into monotonic ones by the effects of ηη, HH and MM.•The formation of SWS may be possible in the interior of white dwarf stars.

The nonlinear theory of two-dimensional ion-acoustic (IA) solitary waves and shocks (SWS) is revisited in a dissipative quantum plasma. The effects of dispersion, caused by the charge separation of electrons and ions and the quantum force associated with the Bohm potential for degenerate electrons, as well as, the dissipation due to the ion kinematic viscosity are considered. Using the reductive perturbation technique, a Kadomtsev–Petviashvili–Burgers (KPB)-type equation, which governs the evolution of small-amplitude SWS in quantum plasmas, is derived, and its different solutions are obtained and analyzed. It is shown that the KPB equation can admit either compressive or rarefactive SWS according to when H≶2/3H≶2/3, or the particle number density satisfies n0≷1.3×1031cm−3, where HH is the ratio of the electron plasmon energy to the Fermi energy densities. Furthermore, the properties of large-amplitude stationary shocks are studied numerically in the case when the wave dispersion due to charge separation is negligible. It is also shown that a transition from monotonic to oscillatory shocks occurs by the effects of the quantum parameter HH.