Hetero-Bäcklund transformation and similarity reduction of an extended (2+1)-dimensional coupled Burgers system in fluid mechanics

Nowadays, the Burgers-type equations are seen in plasma astrophysics, ocean dynamics, atmospheric science, computational fluid mechanics, cosmology, condensed matter physics, statistical physics, nonlinear acoustics, vehicular traffic, electronic transport, and so forth. In this Letter, we investigate an extended (2+1)-dimensional coupled Burgers system in fluid mechanics. With symbolic computation and with reference to the velocity components in fluid-related problems, we construct a hetero-Bäcklund transformation and a similarity reduction, depending on the coefficients in the system. •Burgers-type equations model oceanography, gas dynamics, shock-wave formation, etc.•We study an extended (2+1)-dimensional coupled Burgers system in fluid mechanics.•With reference to the velocity components in fluid-related problems.•We construct a hetero-Backlund transformation and a similarity reduction.•Results depend on the coefficients in the system, with symbolic computation.