Recent manifold contributions have been made to the nonlinear partial differential equations in fluid mechanics, plasma astrophysics, optical fiber communication, chemistry, etc., while people have known that most of the baryonic matter in the Universe is believed to exist as the plasmas. Hereby, with symbolic computation, we investigate a variable-coefficient \((2\!\!+\!\!1)\) -dimensional Zakharov-Kuznetsov-Burgers equation for such cosmic-plasma environments as the neutron stars/pulsar magnetospheres, relativistic jets from the nuclei of active galaxies and quasars, early Universe, center of the Milky Way, white dwarfs, planetary rings, comets, Earth’s auroral zone, interstellar molecular clouds, circumstellar disks and Earth’s ionosphere. Through a noncharacteristic movable singular manifold, auto-Bäcklund transformation and solitons are gotten for the electrostatic wave potential or low-frequency dust-ion-acoustic electrostatic potential, leaning upon such cosmic-plasma coefficient functions as the dispersion, nonlinearity and dissipation coefficients, which are related to, for example, the ion plasma frequency, ion cyclotron frequency, viscosity of the ion fluid, positron density, photoelectron density, electron density, ion temperature, electron temperature, mass of an ion, mass of a dust particle, and interaction frequency between the ions and dust particles.
