Cosmic dusty plasmas via a (3+1)-dimensional generalized variable-coefficient Kadomtsev-Petviashvili-Burgers-type equation: auto-Bäcklund transformations, solitons and similarity reductions plus observational/experimental supports.

Cosmic plasmas are considered as the most abundant form of ordinary matter in the Universe while observations of the cosmic dust in different regions provide an insight into the Universe's recycling processes. For different types of the cosmic dusty plasmas, we hereby, with the symbolic computation and observational/experimental supports, study a (3+1)-dimensional generalized variable-coefficient Kadomtsev-Petviashvili-Burgers-type equation, which can describe the electron-acoustic, dust-acoustic, positron-acoustic, dust-magneto-acoustic, ion-acoustic, magneto-acoustic, ion, quantum-dust-ion-acoustic or dust-ion-acoustic waves in one of the cosmic/laboratory dusty plasmas. With respect to the fluctuation of the electron or ion density, or perturbation of the magnitude of the magnetic field, or electrostatic wave potential, or radial-direction component of the velocity of ions or dust particles, a set of the auto-Bäcklund transformations, several soliton families and a set of the similarity reductions are symbolically computed out, depending on the variable coefficients which represent the dispersion, nonlinearity, geometric effect, Burgers/dusty-fluid-viscosity dissipation and diffraction/transverse perturbation. Variable-coefficient constraints on the soliton solutions are presented. Our analytic results are in agreement with those dusty-plasma-experimentally reported. Future dusty-plasma experiments and observations might justify some other effects hereby offered. [ABSTRACT FROM AUTHOR]